%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP183-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n011.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 16:53:38 EDT 2024

% Result   : Unsatisfiable 2.46s 2.65s
% Output   : Proof 3.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14  % Problem    : GRP183-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.16/0.16  % Command    : do_cvc5 %s %d
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Sun May 26 19:45:24 EDT 2024
% 0.23/0.38  % CPUTime    : 
% 0.23/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.51  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.46/2.65  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.eo9kAMovwd/cvc5---1.0.5_9508.smt2
% 2.46/2.65  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.eo9kAMovwd/cvc5---1.0.5_9508.smt2
% 3.65/3.91  (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 3.65/3.91  (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 3.65/3.91  (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.65/3.91  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 3.65/3.91  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 3.65/3.91  (assume a5 (forall ((X $$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))))
% 3.65/3.91  (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 3.65/3.91  (assume a7 (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)))
% 3.65/3.91  (assume a8 (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)))
% 3.65/3.91  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)))
% 3.65/3.91  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)))
% 3.65/3.91  (assume a11 (forall ((X $$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)))))
% 3.65/3.91  (assume a12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 3.65/3.91  (assume a13 (forall ((Y $$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)))))
% 3.65/3.91  (assume a14 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 3.65/3.91  (assume a15 (= (tptp.inverse tptp.identity) tptp.identity))
% 3.65/3.91  (assume a16 (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)))
% 3.65/3.91  (assume a17 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 3.65/3.91  (assume a18 (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)))
% 3.65/3.91  (step t1 (cl (not (= (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))))) (not (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule equiv_pos2)
% 3.65/3.91  (step t2 (cl (= (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= tptp.identity (tptp.inverse tptp.identity))))) :rule refl)
% 3.65/3.91  (step t3 (cl (= (= (= (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) true) (= (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule equiv_simplify)
% 3.65/3.91  (step t4 (cl (not (= (= (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) true)) (= (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule equiv1 :premises (t3))
% 3.65/3.91  (step t5 (cl (= (= (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))))) :rule all_simplify)
% 3.65/3.91  (step t6 (cl (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule refl)
% 3.65/3.91  (step t7 (cl (= (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule all_simplify)
% 3.65/3.91  (step t8 (cl (= (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule cong :premises (t6 t7))
% 3.65/3.91  (step t9 (cl (= (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) true)) :rule all_simplify)
% 3.65/3.91  (step t10 (cl (= (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) true)) :rule trans :premises (t8 t9))
% 3.65/3.91  (step t11 (cl (= (= (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) true)) :rule trans :premises (t5 t10))
% 3.65/3.91  (step t12 (cl (= (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t4 t11))
% 3.65/3.91  (step t13 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))))) :rule refl)
% 3.65/3.91  (step t14 (cl (= (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule refl)
% 3.65/3.91  (step t15 (cl (= (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule refl)
% 3.65/3.91  (step t16 (cl (= (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))))) :rule refl)
% 3.65/3.91  (step t17 (cl (= (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule refl)
% 3.65/3.91  (step t18 (cl (= (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule refl)
% 3.65/3.91  (step t19 (cl (= (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule refl)
% 3.65/3.91  (step t20 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))))) :rule refl)
% 3.65/3.91  (step t21 (cl (= (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))))) :rule refl)
% 3.65/3.91  (step t22 (cl (= (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule refl)
% 3.65/3.91  (step t23 (cl (= (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule refl)
% 3.65/3.91  (step t24 (cl (= (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule refl)
% 3.65/3.91  (step t25 (cl (= (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t26 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t27 (cl (= (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t28 (cl (= (not (= (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 refl)
% 3.65/3.91  (step t29 (cl (= (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.a)) (tptp.inverse tptp.a)))))) :rule refl)
% 3.65/3.91  (step t30 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t31 (cl (= (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))))) :rule refl)
% 3.65/3.91  (step t32 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t33 (cl (= (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))))) :rule refl)
% 3.65/3.91  (step t34 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t35 (cl (= (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))))) :rule refl)
% 3.65/3.91  (step t36 (cl (= (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule refl)
% 3.65/3.91  (step t37 (cl (= (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))))) :rule refl)
% 3.65/3.91  (step t38 (cl (= (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))))) :rule refl)
% 3.65/3.91  (step t39 (cl (= (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))))) :rule refl)
% 3.65/3.91  (step t40 (cl (= (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t41 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t42 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))))) :rule refl)
% 3.65/3.91  (step t43 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))))) :rule refl)
% 3.65/3.91  (step t44 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule refl)
% 3.65/3.91  (step t45 (cl (= (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))))) :rule refl)
% 3.65/3.91  (step t46 (cl (= (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t47 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t48 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t49 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t50 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule refl)
% 3.65/3.91  (step t51 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))))) :rule refl)
% 3.65/3.91  (step t52 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t53 (cl (= (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t54 (cl (= (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))))) :rule refl)
% 3.65/3.91  (step t55 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t56 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t57 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t58 (cl (= (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule refl)
% 3.65/3.91  (step t59 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t60 (cl (= (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))))) :rule refl)
% 3.65/3.91  (step t61 (cl (= (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))))) :rule refl)
% 3.65/3.91  (step t62 (cl (= (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t63 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t64 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t65 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t66 (cl (= (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))))) :rule refl)
% 3.65/3.91  (step t67 (cl (= (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))))) :rule refl)
% 3.65/3.91  (step t68 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t69 (cl (= (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))))) :rule refl)
% 3.65/3.91  (step t70 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t71 (cl (= (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))))) :rule refl)
% 3.65/3.91  (step t72 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t73 (cl (= (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))))) :rule refl)
% 3.65/3.91  (step t74 (cl (= (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t75 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t76 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t77 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t78 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule refl)
% 3.65/3.91  (step t79 (cl (= (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))))) :rule refl)
% 3.65/3.91  (step t80 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t81 (cl (= (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))))) :rule refl)
% 3.65/3.91  (step t82 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t83 (cl (= (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t84 (cl (= (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t85 (cl (= (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))))) :rule refl)
% 3.65/3.91  (step t86 (cl (= (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))))) :rule refl)
% 3.65/3.91  (step t87 (cl (= (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t88 (cl (= (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))) :rule refl)
% 3.65/3.91  (step t89 (cl (= (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))))) :rule refl)
% 3.65/3.91  (step t90 (cl (= (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule refl)
% 3.65/3.91  (step t91 (cl (= (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule refl)
% 3.65/3.91  (step t92 (cl (= (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))))) :rule cong :premises (t2 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))
% 3.65/3.91  (step t93 (cl (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule and_neg)
% 3.65/3.91  (step t94 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule implies_neg1)
% 3.65/3.91  (anchor :step t95)
% 3.65/3.91  (assume t95.a0 (= tptp.identity (tptp.inverse tptp.identity)))
% 3.65/3.91  (assume t95.a1 (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))
% 3.65/3.91  (assume t95.a2 (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))
% 3.65/3.91  (assume t95.a3 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 3.65/3.91  (assume t95.a4 (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))
% 3.65/3.91  (assume t95.a5 (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)))
% 3.65/3.91  (assume t95.a6 (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))
% 3.65/3.91  (assume t95.a7 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))
% 3.65/3.91  (assume t95.a8 (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 3.65/3.91  (assume t95.a9 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))))
% 3.65/3.91  (assume t95.a10 (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))
% 3.65/3.91  (assume t95.a11 (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 3.65/3.91  (assume t95.a12 (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.a13 (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))
% 3.65/3.91  (assume t95.a14 (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a15 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.a16 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a17 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 3.65/3.91  (assume t95.a18 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 3.65/3.91  (assume t95.a19 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a20 (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))
% 3.65/3.91  (assume t95.a21 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.65/3.91  (assume t95.a22 (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)))
% 3.65/3.91  (assume t95.a23 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a24 (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)))
% 3.65/3.91  (assume t95.a25 (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 3.65/3.91  (assume t95.a26 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.a27 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))))
% 3.65/3.91  (assume t95.a28 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))
% 3.65/3.91  (assume t95.a29 (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.a30 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.a31 (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))))
% 3.65/3.91  (assume t95.a32 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))))
% 3.65/3.91  (assume t95.a33 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.a34 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 3.65/3.91  (assume t95.a35 (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a36 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.a37 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.a38 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.a39 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.a40 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))))
% 3.65/3.91  (assume t95.a41 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a42 (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a43 (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)))
% 3.65/3.91  (assume t95.a44 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a45 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.65/3.91  (assume t95.a46 (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.65/3.91  (assume t95.a47 (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.a48 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.65/3.91  (assume t95.a49 (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.a50 (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.a51 (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.a52 (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.a53 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a54 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a55 (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))
% 3.65/3.91  (assume t95.a56 (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))))
% 3.65/3.91  (assume t95.a57 (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.65/3.91  (assume t95.a58 (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.a59 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.65/3.91  (assume t95.a60 (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))
% 3.65/3.91  (assume t95.a61 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.a62 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))
% 3.65/3.91  (assume t95.a63 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.65/3.91  (assume t95.a64 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a65 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.a66 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a67 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.a68 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))))
% 3.65/3.91  (assume t95.a69 (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a70 (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.a71 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.65/3.91  (assume t95.a72 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a73 (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))
% 3.65/3.91  (assume t95.a74 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))))
% 3.65/3.91  (assume t95.a75 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))
% 3.65/3.91  (assume t95.a76 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.a77 (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))
% 3.65/3.91  (assume t95.a78 (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))
% 3.65/3.91  (assume t95.a79 (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 3.65/3.91  (step t95.t1 (cl (=> (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule implies_neg1)
% 3.65/3.91  (anchor :step t95.t2)
% 3.65/3.91  (assume t95.t2.a0 (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))
% 3.65/3.91  (assume t95.t2.a1 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a2 (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))
% 3.65/3.91  (assume t95.t2.a3 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 3.65/3.91  (assume t95.t2.a4 (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 3.65/3.91  (assume t95.t2.a5 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.t2.a6 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.65/3.91  (assume t95.t2.a7 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))
% 3.65/3.91  (assume t95.t2.a8 (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))
% 3.65/3.91  (assume t95.t2.a9 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.t2.a10 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.65/3.91  (assume t95.t2.a11 (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 3.65/3.91  (assume t95.t2.a12 (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))
% 3.65/3.91  (assume t95.t2.a13 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 3.65/3.91  (assume t95.t2.a14 (= tptp.identity (tptp.inverse tptp.identity)))
% 3.65/3.91  (assume t95.t2.a15 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a16 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a17 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 3.65/3.91  (assume t95.t2.a18 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))
% 3.65/3.91  (assume t95.t2.a19 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.t2.a20 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.65/3.91  (assume t95.t2.a21 (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 3.65/3.91  (assume t95.t2.a22 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.t2.a23 (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.t2.a24 (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))))
% 3.65/3.91  (assume t95.t2.a25 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))
% 3.65/3.91  (assume t95.t2.a26 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))))
% 3.65/3.91  (assume t95.t2.a27 (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)))
% 3.65/3.91  (assume t95.t2.a28 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 3.65/3.91  (assume t95.t2.a29 (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a30 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))))
% 3.65/3.91  (assume t95.t2.a31 (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))
% 3.65/3.91  (assume t95.t2.a32 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))))
% 3.65/3.91  (assume t95.t2.a33 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a34 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a35 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))))
% 3.65/3.91  (assume t95.t2.a36 (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.t2.a37 (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))))
% 3.65/3.91  (assume t95.t2.a38 (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a39 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a40 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.65/3.91  (assume t95.t2.a41 (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))
% 3.65/3.91  (assume t95.t2.a42 (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a43 (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a44 (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a45 (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a46 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a47 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.t2.a48 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a49 (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)))
% 3.65/3.91  (assume t95.t2.a50 (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)))
% 3.65/3.91  (assume t95.t2.a51 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a52 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))))
% 3.65/3.91  (assume t95.t2.a53 (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.t2.a54 (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))
% 3.65/3.91  (assume t95.t2.a55 (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.t2.a56 (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.t2.a57 (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a58 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.t2.a59 (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))
% 3.65/3.91  (assume t95.t2.a60 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))))
% 3.65/3.91  (assume t95.t2.a61 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a62 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a63 (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a64 (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))
% 3.65/3.91  (assume t95.t2.a65 (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a66 (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))
% 3.65/3.91  (assume t95.t2.a67 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a68 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.65/3.91  (assume t95.t2.a69 (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a70 (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a71 (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.t2.a72 (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))
% 3.65/3.91  (assume t95.t2.a73 (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)))
% 3.65/3.91  (assume t95.t2.a74 (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))
% 3.65/3.91  (assume t95.t2.a75 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a76 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))
% 3.65/3.91  (assume t95.t2.a77 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.65/3.91  (assume t95.t2.a78 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))
% 3.65/3.91  (assume t95.t2.a79 (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))
% 3.65/3.91  (step t95.t2.t1 (cl (= (= (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)) false) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule equiv_simplify)
% 3.65/3.91  (step t95.t2.t2 (cl (not (= (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)) false)) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule equiv1 :premises (t95.t2.t1))
% 3.65/3.91  (step t95.t2.t3 (cl (= (tptp.inverse tptp.a) (tptp.inverse tptp.a))) :rule refl)
% 3.65/3.91  (step t95.t2.t4 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t95.t2.a63))
% 3.65/3.91  (step t95.t2.t5 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t4))
% 3.65/3.91  (step t95.t2.t6 (cl (= tptp.a tptp.a)) :rule refl)
% 3.65/3.91  (step t95.t2.t7 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)) :rule symm :premises (t95.t2.a3))
% 3.65/3.91  (step t95.t2.t8 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.inverse tptp.identity))) :rule cong :premises (t95.t2.t7))
% 3.65/3.91  (step t95.t2.t9 (cl (= (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t95.t2.t8))
% 3.65/3.91  (step t95.t2.t10 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t7 t95.t2.a14 t95.t2.t9 t95.t2.a15))
% 3.65/3.91  (step t95.t2.t11 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t6 t95.t2.t10))
% 3.65/3.91  (step t95.t2.t12 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.a31))
% 3.65/3.91  (step t95.t2.t13 (cl (= (tptp.inverse (tptp.inverse tptp.a)) tptp.a)) :rule symm :premises (t95.t2.a28))
% 3.65/3.91  (step t95.t2.t14 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.t13))
% 3.65/3.91  (step t95.t2.t15 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t14 t95.t2.t3))
% 3.65/3.91  (step t95.t2.t16 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.t15))
% 3.65/3.91  (step t95.t2.t17 (cl (= tptp.identity (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule trans :premises (t95.t2.a17 t95.t2.t16))
% 3.65/3.91  (step t95.t2.t18 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t95.t2.t17))
% 3.65/3.91  (step t95.t2.t19 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.identity tptp.a))) :rule cong :premises (t95.t2.t18 t95.t2.t13))
% 3.65/3.91  (step t95.t2.t20 (cl (= tptp.identity tptp.identity)) :rule refl)
% 3.65/3.91  (step t95.t2.t21 (cl (= (tptp.multiply tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t20 t95.t2.t14))
% 3.65/3.91  (step t95.t2.t22 (cl (= (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a29))
% 3.65/3.91  (step t95.t2.t23 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) tptp.a)) :rule trans :premises (t95.t2.t11 t95.t2.t12 t95.t2.t19 t95.t2.t21 t95.t2.t22 t95.t2.t13))
% 3.65/3.91  (step t95.t2.t24 (cl (= tptp.a (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t95.t2.t23))
% 3.65/3.91  (step t95.t2.t25 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) :rule symm :premises (t95.t2.a5))
% 3.65/3.91  (step t95.t2.t26 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.inverse tptp.a))) :rule symm :premises (t95.t2.a4))
% 3.65/3.91  (step t95.t2.t27 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule cong :premises (t95.t2.t26 t95.t2.t6))
% 3.65/3.91  (step t95.t2.t28 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t25 t95.t2.t27 t95.t2.t7 t95.t2.a14 t95.t2.t9 t95.t2.a15))
% 3.65/3.91  (step t95.t2.t29 (cl (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t6 t95.t2.t28))
% 3.65/3.91  (step t95.t2.t30 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.t29))
% 3.65/3.91  (step t95.t2.t31 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.a9))
% 3.65/3.91  (step t95.t2.t32 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule refl)
% 3.65/3.91  (step t95.t2.t33 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t95.t2.a8))
% 3.65/3.91  (step t95.t2.t34 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule cong :premises (t95.t2.t32 t95.t2.t33))
% 3.65/3.91  (step t95.t2.t35 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) :rule symm :premises (t95.t2.a7))
% 3.65/3.91  (step t95.t2.t36 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) :rule cong :premises (t95.t2.t32 t95.t2.t35))
% 3.65/3.91  (step t95.t2.t37 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) :rule trans :premises (t95.t2.t31 t95.t2.t34 t95.t2.t36))
% 3.65/3.91  (step t95.t2.t38 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.t37))
% 3.65/3.91  (step t95.t2.t39 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule cong :premises (t95.t2.t6 t95.t2.t38))
% 3.65/3.91  (step t95.t2.t40 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.a45))
% 3.65/3.91  (step t95.t2.t41 (cl (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.t40))
% 3.65/3.91  (step t95.t2.t42 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule trans :premises (t95.t2.t39 t95.t2.t41))
% 3.65/3.91  (step t95.t2.t43 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule refl)
% 3.65/3.91  (step t95.t2.t44 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule cong :premises (t95.t2.t42 t95.t2.t43))
% 3.65/3.91  (step t95.t2.t45 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule symm :premises (t95.t2.a44))
% 3.65/3.91  (step t95.t2.t46 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t95.t2.a19))
% 3.65/3.91  (step t95.t2.t47 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t3 t95.t2.a17))
% 3.65/3.91  (step t95.t2.t48 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a16))
% 3.65/3.91  (step t95.t2.t49 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t95.t2.a15))
% 3.65/3.91  (step t95.t2.t50 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.identity))) :rule trans :premises (t95.t2.t49 t95.t2.t8))
% 3.65/3.91  (step t95.t2.t51 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t50 t95.t2.t3))
% 3.65/3.91  (step t95.t2.t52 (cl (= (tptp.inverse tptp.identity) tptp.identity)) :rule symm :premises (t95.t2.a14))
% 3.65/3.91  (step t95.t2.t53 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t52 t95.t2.t3))
% 3.65/3.91  (step t95.t2.t54 (cl (= (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) :rule symm :premises (t95.t2.a13))
% 3.65/3.91  (step t95.t2.t55 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.identity) (tptp.inverse tptp.a))) :rule trans :premises (t95.t2.t47 t95.t2.t48 t95.t2.t51 t95.t2.t53 t95.t2.t54))
% 3.65/3.91  (step t95.t2.t56 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t7 t95.t2.t55))
% 3.65/3.91  (step t95.t2.t57 (cl (= (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t95.t2.t56))
% 3.65/3.91  (step t95.t2.t58 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t95.t2.a18))
% 3.65/3.91  (step t95.t2.t59 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule trans :premises (t95.t2.a12 t95.t2.t57 t95.t2.t58))
% 3.65/3.91  (step t95.t2.t60 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule symm :premises (t95.t2.t59))
% 3.65/3.91  (step t95.t2.t61 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) :rule refl)
% 3.65/3.91  (step t95.t2.t62 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule cong :premises (t95.t2.t60 t95.t2.t61))
% 3.65/3.91  (step t95.t2.t63 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule trans :premises (t95.t2.t46 t95.t2.t62))
% 3.65/3.91  (step t95.t2.t64 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule symm :premises (t95.t2.t63))
% 3.65/3.91  (step t95.t2.t65 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule cong :premises (t95.t2.t6 t95.t2.t64))
% 3.65/3.91  (step t95.t2.t66 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule symm :premises (t95.t2.a41))
% 3.65/3.91  (step t95.t2.t67 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule refl)
% 3.65/3.91  (step t95.t2.t68 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule cong :premises (t95.t2.t18 t95.t2.t67))
% 3.65/3.91  (step t95.t2.t69 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t95.t2.a40))
% 3.65/3.91  (step t95.t2.t70 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule symm :premises (t95.t2.a11))
% 3.65/3.91  (step t95.t2.t71 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t95.t2.a22))
% 3.65/3.91  (step t95.t2.t72 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule symm :premises (t95.t2.a21))
% 3.65/3.91  (step t95.t2.t73 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t95.t2.t72))
% 3.65/3.91  (step t95.t2.t74 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule cong :premises (t95.t2.t26 t95.t2.t32))
% 3.65/3.91  (step t95.t2.t75 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.inverse tptp.a))) :rule trans :premises (t95.t2.t73 t95.t2.t74 t95.t2.t26))
% 3.65/3.91  (step t95.t2.t76 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule cong :premises (t95.t2.t75 t95.t2.t61))
% 3.65/3.91  (step t95.t2.t77 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t95.t2.t58))
% 3.65/3.91  (step t95.t2.t78 (cl (= (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule symm :premises (t95.t2.a12))
% 3.65/3.91  (step t95.t2.t79 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule trans :premises (t95.t2.t71 t95.t2.t76 t95.t2.t77 t95.t2.t56 t95.t2.t78))
% 3.65/3.91  (step t95.t2.t80 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule symm :premises (t95.t2.t79))
% 3.65/3.91  (step t95.t2.t81 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule trans :premises (t95.t2.t70 t95.t2.t80))
% 3.65/3.91  (step t95.t2.t82 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.a14 t95.t2.t9 t95.t2.a15))
% 3.65/3.91  (step t95.t2.t83 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t6 t95.t2.t82))
% 3.65/3.91  (step t95.t2.t84 (cl (= (tptp.multiply tptp.a tptp.identity) tptp.a)) :rule trans :premises (t95.t2.t83 t95.t2.t12 t95.t2.t19 t95.t2.t21 t95.t2.t22 t95.t2.t13))
% 3.65/3.91  (step t95.t2.t85 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) tptp.a))) :rule cong :premises (t95.t2.t81 t95.t2.t84))
% 3.65/3.91  (step t95.t2.t86 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule cong :premises (t95.t2.t79 t95.t2.a7))
% 3.65/3.91  (step t95.t2.t87 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) :rule symm :premises (t95.t2.a30))
% 3.65/3.91  (step t95.t2.t88 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule symm :premises (t95.t2.t87))
% 3.65/3.91  (step t95.t2.t89 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.identity))) :rule trans :premises (t95.t2.t7 t95.t2.a14))
% 3.65/3.91  (step t95.t2.t90 (cl (= (tptp.multiply tptp.identity tptp.a) tptp.a)) :rule trans :premises (t95.t2.t21 t95.t2.t22 t95.t2.t13))
% 3.65/3.91  (step t95.t2.t91 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.least_upper_bound (tptp.inverse tptp.identity) tptp.a))) :rule cong :premises (t95.t2.t89 t95.t2.t90))
% 3.65/3.91  (step t95.t2.t92 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity tptp.a))) :rule cong :premises (t95.t2.t52 t95.t2.t6))
% 3.65/3.91  (step t95.t2.t93 (cl (= (tptp.least_upper_bound tptp.identity tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) :rule symm :premises (t95.t2.a27))
% 3.65/3.91  (step t95.t2.t94 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) :rule trans :premises (t95.t2.t85 t95.t2.t86 t95.t2.t36 t95.t2.t88 t95.t2.t91 t95.t2.t92 t95.t2.t93))
% 3.65/3.91  (step t95.t2.t95 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule cong :premises (t95.t2.t61 t95.t2.t94))
% 3.65/3.91  (step t95.t2.t96 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule symm :premises (t95.t2.t95))
% 3.65/3.91  (step t95.t2.t97 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) :rule trans :premises (t95.t2.t88 t95.t2.t91 t95.t2.t92 t95.t2.t93))
% 3.65/3.91  (step t95.t2.t98 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule refl)
% 3.65/3.91  (step t95.t2.t99 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule cong :premises (t95.t2.t97 t95.t2.t98))
% 3.65/3.91  (step t95.t2.t100 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule symm :premises (t95.t2.t99))
% 3.65/3.91  (step t95.t2.t101 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) :rule symm :premises (t95.t2.t97))
% 3.65/3.91  (step t95.t2.t102 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule symm :premises (t95.t2.t36))
% 3.65/3.91  (step t95.t2.t103 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) tptp.a))) :rule symm :premises (t95.t2.t86))
% 3.65/3.91  (step t95.t2.t104 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule symm :premises (t95.t2.t85))
% 3.65/3.91  (step t95.t2.t105 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule trans :premises (t95.t2.t102 t95.t2.t103 t95.t2.t104))
% 3.65/3.91  (step t95.t2.t106 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule cong :premises (t95.t2.t101 t95.t2.t105))
% 3.65/3.91  (step t95.t2.t107 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.t106))
% 3.65/3.91  (step t95.t2.t108 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule trans :premises (t95.t2.t65 t95.t2.t66 t95.t2.t68 t95.t2.t69 t95.t2.t96 t95.t2.t100 t95.t2.t107))
% 3.65/3.91  (step t95.t2.t109 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a34))
% 3.65/3.91  (step t95.t2.t110 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t109))
% 3.65/3.91  (step t95.t2.t111 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a33))
% 3.65/3.91  (step t95.t2.t112 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t111))
% 3.65/3.91  (step t95.t2.t113 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) :rule refl)
% 3.65/3.91  (step t95.t2.t114 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t95.t2.a17))
% 3.65/3.91  (step t95.t2.t115 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity))) :rule cong :premises (t95.t2.t113 t95.t2.t114))
% 3.65/3.91  (step t95.t2.t116 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity))) :rule symm :premises (t95.t2.a32))
% 3.65/3.91  (step t95.t2.t117 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule symm :premises (t95.t2.t116))
% 3.65/3.91  (step t95.t2.t118 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t95.t2.t70))
% 3.65/3.91  (step t95.t2.t119 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.a tptp.identity))) :rule refl)
% 3.65/3.91  (step t95.t2.t120 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule cong :premises (t95.t2.t118 t95.t2.t119))
% 3.65/3.91  (step t95.t2.t121 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity)))) :rule trans :premises (t95.t2.t112 t95.t2.t115 t95.t2.t117 t95.t2.t120))
% 3.65/3.91  (step t95.t2.t122 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule cong :premises (t95.t2.t101 t95.t2.t121))
% 3.65/3.91  (step t95.t2.t123 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))))) :rule trans :premises (t95.t2.t110 t95.t2.t122))
% 3.65/3.91  (step t95.t2.t124 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.t123))
% 3.65/3.91  (step t95.t2.t125 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)))) :rule trans :premises (t95.t2.t108 t95.t2.t106 t95.t2.t124))
% 3.65/3.91  (step t95.t2.t126 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.a43))
% 3.65/3.91  (step t95.t2.t127 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.a42))
% 3.65/3.91  (step t95.t2.t128 (cl (= (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule cong :premises (t95.t2.t6 t95.t2.a36))
% 3.65/3.91  (step t95.t2.t129 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound tptp.a tptp.a))) :rule symm :premises (t95.t2.t128))
% 3.65/3.91  (step t95.t2.t130 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule symm :premises (t95.t2.a37))
% 3.65/3.91  (step t95.t2.t131 (cl (= (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.a)) :rule symm :premises (t95.t2.a36))
% 3.65/3.91  (step t95.t2.t132 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t131 t95.t2.t82))
% 3.65/3.91  (step t95.t2.t133 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) tptp.a)) :rule trans :premises (t95.t2.t130 t95.t2.t132 t95.t2.t12 t95.t2.t19 t95.t2.t21 t95.t2.t22 t95.t2.t13))
% 3.65/3.91  (step t95.t2.t134 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (tptp.greatest_lower_bound tptp.a tptp.a))) :rule cong :premises (t95.t2.t84 t95.t2.t133))
% 3.65/3.91  (step t95.t2.t135 (cl (= (tptp.greatest_lower_bound tptp.a tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))))) :rule symm :premises (t95.t2.t134))
% 3.65/3.91  (step t95.t2.t136 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a38))
% 3.65/3.91  (step t95.t2.t137 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t136))
% 3.65/3.91  (step t95.t2.t138 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t114 t95.t2.a14 t95.t2.t9 t95.t2.a15))
% 3.65/3.91  (step t95.t2.t139 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t6 t95.t2.t138))
% 3.65/3.91  (step t95.t2.t140 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply tptp.a tptp.identity))) :rule symm :premises (t95.t2.t83))
% 3.65/3.91  (step t95.t2.t141 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a tptp.identity))) :rule trans :premises (t95.t2.t137 t95.t2.t139 t95.t2.t140))
% 3.65/3.91  (step t95.t2.t142 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule symm :premises (t95.t2.t132))
% 3.65/3.91  (step t95.t2.t143 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule trans :premises (t95.t2.t137 t95.t2.t139 t95.t2.t142 t95.t2.a37))
% 3.65/3.91  (step t95.t2.t144 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))))) :rule cong :premises (t95.t2.t141 t95.t2.t143))
% 3.65/3.91  (step t95.t2.t145 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t144))
% 3.65/3.91  (step t95.t2.t146 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a39))
% 3.65/3.91  (step t95.t2.t147 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)))) :rule trans :premises (t95.t2.t126 t95.t2.t127 t95.t2.t29 t95.t2.t12 t95.t2.t19 t95.t2.t21 t95.t2.t22 t95.t2.t13 t95.t2.a35 t95.t2.t129 t95.t2.t135 t95.t2.t145 t95.t2.t146))
% 3.65/3.91  (step t95.t2.t148 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t125 t95.t2.t147))
% 3.65/3.91  (step t95.t2.t149 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule trans :premises (t95.t2.t99 t95.t2.t95))
% 3.65/3.91  (step t95.t2.t150 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule trans :premises (t95.t2.t123 t95.t2.t149))
% 3.65/3.91  (step t95.t2.t151 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t146))
% 3.65/3.91  (step t95.t2.t152 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) tptp.a)) :rule symm :premises (t95.t2.a35))
% 3.65/3.91  (step t95.t2.t153 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) tptp.a)) :rule trans :premises (t95.t2.t151 t95.t2.t144 t95.t2.t134 t95.t2.t128 t95.t2.t152))
% 3.65/3.91  (step t95.t2.t154 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a))) :rule cong :premises (t95.t2.t150 t95.t2.t153))
% 3.65/3.91  (step t95.t2.t155 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a))) :rule trans :premises (t95.t2.t11 t95.t2.t30 t95.t2.a42 t95.t2.a43 t95.t2.t44 t95.t2.t45 t95.t2.t148 t95.t2.t154))
% 3.65/3.91  (step t95.t2.t156 (cl (= tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a))) :rule trans :premises (t95.t2.t24 t95.t2.t155))
% 3.65/3.91  (step t95.t2.t157 (cl (= tptp.a (tptp.multiply tptp.a tptp.identity))) :rule symm :premises (t95.t2.t84))
% 3.65/3.91  (step t95.t2.t158 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.t152 t95.t2.t113))
% 3.65/3.91  (step t95.t2.t159 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.t158))
% 3.65/3.91  (step t95.t2.t160 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule trans :premises (t95.t2.t83 t95.t2.t30 t95.t2.a42 t95.t2.a43))
% 3.65/3.91  (step t95.t2.t161 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule trans :premises (t95.t2.t152 t95.t2.t157 t95.t2.t160))
% 3.65/3.91  (step t95.t2.t162 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.t161 t95.t2.t113))
% 3.65/3.91  (step t95.t2.t163 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.a62))
% 3.65/3.91  (step t95.t2.t164 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.t163))
% 3.65/3.91  (step t95.t2.t165 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule trans :premises (t95.t2.t159 t95.t2.t162 t95.t2.t164))
% 3.65/3.91  (step t95.t2.t166 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule cong :premises (t95.t2.t165 t95.t2.t43))
% 3.65/3.91  (step t95.t2.t167 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule symm :premises (t95.t2.a61))
% 3.65/3.91  (step t95.t2.t168 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule refl)
% 3.65/3.91  (step t95.t2.t169 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity))) :rule symm :premises (t95.t2.a60))
% 3.65/3.91  (step t95.t2.t170 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule cong :premises (t95.t2.t89 t95.t2.t20))
% 3.65/3.91  (step t95.t2.t171 (cl (= (tptp.multiply (tptp.inverse tptp.identity) tptp.identity) tptp.identity)) :rule symm :premises (t95.t2.a59))
% 3.65/3.91  (step t95.t2.t172 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.inverse tptp.identity))) :rule trans :premises (t95.t2.t169 t95.t2.t170 t95.t2.t171 t95.t2.a14))
% 3.65/3.91  (step t95.t2.t173 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.t172 t95.t2.t113))
% 3.65/3.91  (step t95.t2.t174 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.t52 t95.t2.t113))
% 3.65/3.91  (step t95.t2.t175 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) :rule symm :premises (t95.t2.a47))
% 3.65/3.91  (step t95.t2.t176 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) :rule trans :premises (t95.t2.t173 t95.t2.t174 t95.t2.t175))
% 3.65/3.91  (step t95.t2.t177 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.t168 t95.t2.t176))
% 3.65/3.91  (step t95.t2.t178 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.t177))
% 3.65/3.91  (step t95.t2.t179 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.a49))
% 3.65/3.91  (step t95.t2.t180 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) :rule symm :premises (t95.t2.t179))
% 3.65/3.91  (step t95.t2.t181 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.t3 t95.t2.t101))
% 3.65/3.91  (step t95.t2.t182 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule trans :premises (t95.t2.a12 t95.t2.t57 t95.t2.t58 t95.t2.t181))
% 3.65/3.91  (step t95.t2.t183 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule cong :premises (t95.t2.t14 t95.t2.t182))
% 3.65/3.91  (step t95.t2.t184 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.a48))
% 3.65/3.91  (step t95.t2.t185 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) :rule trans :premises (t95.t2.t114 t95.t2.a14))
% 3.65/3.91  (step t95.t2.t186 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.t185 t95.t2.t113))
% 3.65/3.91  (step t95.t2.t187 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) :rule trans :premises (t95.t2.t183 t95.t2.t184 t95.t2.t186 t95.t2.t174 t95.t2.t175 t95.t2.t88 t95.t2.t91 t95.t2.t92 t95.t2.t93))
% 3.65/3.91  (step t95.t2.t188 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) :rule trans :premises (t95.t2.t187 t95.t2.t101))
% 3.65/3.91  (step t95.t2.t189 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t188 t95.t2.t14))
% 3.65/3.91  (step t95.t2.t190 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t101 t95.t2.t14))
% 3.65/3.91  (step t95.t2.t191 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule symm :premises (t95.t2.t190))
% 3.65/3.91  (step t95.t2.t192 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule cong :premises (t95.t2.t61 t95.t2.t13))
% 3.65/3.91  (step t95.t2.t193 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t192))
% 3.65/3.91  (step t95.t2.t194 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t180 t95.t2.t189 t95.t2.t191 t95.t2.t193))
% 3.65/3.91  (step t95.t2.t195 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) :rule symm :premises (t95.t2.t189))
% 3.65/3.91  (step t95.t2.t196 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.a36 t95.t2.t113))
% 3.65/3.91  (step t95.t2.t197 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.a57))
% 3.65/3.91  (step t95.t2.t198 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.t197))
% 3.65/3.91  (step t95.t2.t199 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.t35 t95.t2.t113))
% 3.65/3.91  (step t95.t2.t200 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule cong :premises (t95.t2.t6 t95.t2.t88))
% 3.65/3.91  (step t95.t2.t201 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule symm :premises (t95.t2.a56))
% 3.65/3.91  (step t95.t2.t202 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule symm :premises (t95.t2.t201))
% 3.65/3.91  (step t95.t2.t203 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule trans :premises (t95.t2.t199 t95.t2.t200 t95.t2.t202))
% 3.65/3.91  (step t95.t2.t204 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule cong :premises (t95.t2.t168 t95.t2.t203))
% 3.65/3.91  (step t95.t2.t205 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule symm :premises (t95.t2.a55))
% 3.65/3.91  (step t95.t2.t206 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule symm :premises (t95.t2.t205))
% 3.65/3.91  (step t95.t2.t207 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule trans :premises (t95.t2.t11 t95.t2.t30 t95.t2.a42 t95.t2.a43))
% 3.65/3.91  (step t95.t2.t208 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule cong :premises (t95.t2.t168 t95.t2.t207))
% 3.65/3.91  (step t95.t2.t209 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.a54))
% 3.65/3.91  (step t95.t2.t210 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule trans :premises (t95.t2.t208 t95.t2.t209))
% 3.65/3.91  (step t95.t2.t211 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule trans :premises (t95.t2.t190 t95.t2.t195 t95.t2.t179))
% 3.65/3.91  (step t95.t2.t212 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule symm :premises (t95.t2.t211))
% 3.65/3.91  (step t95.t2.t213 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule trans :premises (t95.t2.t210 t95.t2.t212))
% 3.65/3.91  (step t95.t2.t214 (cl (= (tptp.multiply tptp.identity tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) :rule trans :premises (t95.t2.t21 t95.t2.t22))
% 3.65/3.91  (step t95.t2.t215 (cl (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity tptp.a))) :rule symm :premises (t95.t2.t214))
% 3.65/3.91  (step t95.t2.t216 (cl (= (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule cong :premises (t95.t2.t84 t95.t2.t215))
% 3.65/3.91  (step t95.t2.t217 (cl (= (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t216))
% 3.65/3.91  (step t95.t2.t218 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t213 t95.t2.t217))
% 3.65/3.91  (step t95.t2.t219 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.t199))
% 3.65/3.91  (step t95.t2.t220 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule trans :premises (t95.t2.t190 t95.t2.t195 t95.t2.t179 t95.t2.t219))
% 3.65/3.91  (step t95.t2.t221 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule cong :premises (t95.t2.t220 t95.t2.t216))
% 3.65/3.91  (step t95.t2.t222 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.a53))
% 3.65/3.91  (step t95.t2.t223 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule cong :premises (t95.t2.t216 t95.t2.t220))
% 3.65/3.91  (step t95.t2.t224 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.t223))
% 3.65/3.91  (step t95.t2.t225 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule trans :premises (t95.t2.t192 t95.t2.t190 t95.t2.t195 t95.t2.t179 t95.t2.t196 t95.t2.t198 t95.t2.t204 t95.t2.t206 t95.t2.t218 t95.t2.t221 t95.t2.t222 t95.t2.t224))
% 3.65/3.91  (step t95.t2.t226 (cl (= (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t6 t95.t2.t214))
% 3.65/3.91  (step t95.t2.t227 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t199 t95.t2.t180 t95.t2.t189))
% 3.65/3.91  (step t95.t2.t228 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t226 t95.t2.t227))
% 3.65/3.91  (step t95.t2.t229 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule trans :premises (t95.t2.t223 t95.t2.t228))
% 3.65/3.91  (step t95.t2.t230 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule trans :premises (t95.t2.t194 t95.t2.t225 t95.t2.t229))
% 3.65/3.91  (step t95.t2.t231 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a))) :rule cong :premises (t95.t2.t59 t95.t2.t35))
% 3.65/3.91  (step t95.t2.t232 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a))) :rule symm :premises (t95.t2.a58))
% 3.65/3.91  (step t95.t2.t233 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.t232))
% 3.65/3.91  (step t95.t2.t234 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule cong :premises (t95.t2.t61 t95.t2.t84))
% 3.65/3.91  (step t95.t2.t235 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule symm :premises (t95.t2.t234))
% 3.65/3.91  (step t95.t2.t236 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.a tptp.identity))))) :rule cong :premises (t95.t2.t3 t95.t2.t235))
% 3.65/3.91  (step t95.t2.t237 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t234 t95.t2.t190))
% 3.65/3.91  (step t95.t2.t238 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t3 t95.t2.t237))
% 3.65/3.91  (step t95.t2.t239 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule trans :premises (t95.t2.t102 t95.t2.t231 t95.t2.t233 t95.t2.t236 t95.t2.t238))
% 3.65/3.91  (step t95.t2.t240 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule cong :premises (t95.t2.t230 t95.t2.t239))
% 3.65/3.91  (step t95.t2.t241 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule symm :premises (t95.t2.a52))
% 3.65/3.91  (step t95.t2.t242 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a51))
% 3.65/3.91  (step t95.t2.t243 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t242))
% 3.65/3.91  (step t95.t2.t244 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) tptp.a)) :rule trans :premises (t95.t2.t141 t95.t2.t84))
% 3.65/3.91  (step t95.t2.t245 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) :rule cong :premises (t95.t2.a7 t95.t2.t20))
% 3.65/3.91  (step t95.t2.t246 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) :rule trans :premises (t95.t2.t112 t95.t2.t115 t95.t2.t117 t95.t2.t120 t95.t2.t85 t95.t2.t86 t95.t2.t36 t95.t2.t88 t95.t2.t91 t95.t2.t92 t95.t2.t93 t95.t2.t245))
% 3.65/3.91  (step t95.t2.t247 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))) (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule cong :premises (t95.t2.t244 t95.t2.t246))
% 3.65/3.91  (step t95.t2.t248 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule symm :premises (t95.t2.a50))
% 3.65/3.91  (step t95.t2.t249 (cl (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule symm :premises (t95.t2.t248))
% 3.65/3.91  (step t95.t2.t250 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) :rule cong :premises (t95.t2.t131 t95.t2.t20))
% 3.65/3.91  (step t95.t2.t251 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound tptp.a tptp.identity))) :rule trans :premises (t95.t2.t243 t95.t2.t247 t95.t2.t249 t95.t2.t250))
% 3.65/3.91  (step t95.t2.t252 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule refl)
% 3.65/3.91  (step t95.t2.t253 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t251 t95.t2.t252))
% 3.65/3.91  (step t95.t2.t254 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t180 t95.t2.t189))
% 3.65/3.91  (step t95.t2.t255 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t61 t95.t2.t254))
% 3.65/3.91  (step t95.t2.t256 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule symm :premises (t95.t2.t255))
% 3.65/3.91  (step t95.t2.t257 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule trans :premises (t95.t2.t177 t95.t2.t240 t95.t2.t241 t95.t2.t253 t95.t2.t256))
% 3.65/3.91  (step t95.t2.t258 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule trans :premises (t95.t2.t178 t95.t2.t257 t95.t2.t255))
% 3.65/3.91  (step t95.t2.t259 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a tptp.identity))) :rule trans :premises (t95.t2.t11 t95.t2.t140))
% 3.65/3.91  (step t95.t2.t260 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule trans :premises (t95.t2.t259 t95.t2.t84 t95.t2.a35))
% 3.65/3.91  (step t95.t2.t261 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule cong :premises (t95.t2.t260 t95.t2.t113))
% 3.65/3.91  (step t95.t2.t262 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule trans :premises (t95.t2.t261 t95.t2.t158))
% 3.65/3.91  (step t95.t2.t263 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule cong :premises (t95.t2.t262 t95.t2.t43))
% 3.65/3.91  (step t95.t2.t264 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.inverse (tptp.inverse tptp.a)))) :rule trans :premises (t95.t2.t263 t95.t2.t126 t95.t2.t127 t95.t2.t29 t95.t2.t12 t95.t2.t19 t95.t2.t21 t95.t2.t22))
% 3.65/3.91  (step t95.t2.t265 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t258 t95.t2.t264))
% 3.65/3.91  (step t95.t2.t266 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t83 t95.t2.t30 t95.t2.a42 t95.t2.a43 t95.t2.t166 t95.t2.t167 t95.t2.t265))
% 3.65/3.91  (step t95.t2.t267 (cl (= tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t157 t95.t2.t266))
% 3.65/3.91  (step t95.t2.t268 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t267 t95.t2.t3))
% 3.65/3.91  (step t95.t2.t269 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a46))
% 3.65/3.91  (step t95.t2.t270 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t269))
% 3.65/3.91  (step t95.t2.t271 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule refl)
% 3.65/3.91  (step t95.t2.t272 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t150 t95.t2.t271))
% 3.65/3.91  (step t95.t2.t273 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t268 t95.t2.t270 t95.t2.t272))
% 3.65/3.91  (step t95.t2.t274 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule cong :premises (t95.t2.t156 t95.t2.t273))
% 3.65/3.91  (step t95.t2.t275 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule trans :premises (t95.t2.t5 t95.t2.t274))
% 3.65/3.91  (step t95.t2.t276 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule cong :premises (t95.t2.t3 t95.t2.t275))
% 3.65/3.91  (step t95.t2.t277 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule symm :premises (t95.t2.a26))
% 3.65/3.91  (step t95.t2.t278 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule symm :premises (t95.t2.t277))
% 3.65/3.91  (step t95.t2.t279 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)))) :rule symm :premises (t95.t2.a20))
% 3.65/3.91  (step t95.t2.t280 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t95.t2.t279))
% 3.65/3.91  (step t95.t2.t281 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule cong :premises (t95.t2.t118 t95.t2.t61))
% 3.65/3.91  (step t95.t2.t282 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule trans :premises (t95.t2.t63 t95.t2.t281))
% 3.65/3.91  (step t95.t2.t283 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) :rule cong :premises (t95.t2.t282 t95.t2.t7))
% 3.65/3.91  (step t95.t2.t284 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t95.t2.t281))
% 3.65/3.91  (step t95.t2.t285 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) :rule symm :premises (t95.t2.t27))
% 3.65/3.91  (step t95.t2.t286 (cl (= tptp.identity (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule trans :premises (t95.t2.a3 t95.t2.t285 t95.t2.a5 t95.t2.a6))
% 3.65/3.91  (step t95.t2.t287 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule cong :premises (t95.t2.t284 t95.t2.t286))
% 3.65/3.91  (step t95.t2.t288 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule symm :premises (t95.t2.a10))
% 3.65/3.91  (step t95.t2.t289 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t95.t2.t288))
% 3.65/3.91  (step t95.t2.t290 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule refl)
% 3.65/3.91  (step t95.t2.t291 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t95.t2.t37 t95.t2.t290))
% 3.65/3.91  (step t95.t2.t292 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.a6))
% 3.65/3.91  (step t95.t2.t293 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) tptp.identity)) :rule trans :premises (t95.t2.t280 t95.t2.t283 t95.t2.t287 t95.t2.t289 t95.t2.t291 t95.t2.t292 t95.t2.t25 t95.t2.t27 t95.t2.t7))
% 3.65/3.91  (step t95.t2.t294 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule symm :premises (t95.t2.a25))
% 3.65/3.91  (step t95.t2.t295 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule symm :premises (t95.t2.t294))
% 3.65/3.91  (step t95.t2.t296 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (tptp.inverse tptp.a))) :rule trans :premises (t95.t2.t48 t95.t2.t51 t95.t2.t53 t95.t2.t54))
% 3.65/3.91  (step t95.t2.t297 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t282 t95.t2.t296))
% 3.65/3.91  (step t95.t2.t298 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule refl)
% 3.65/3.91  (step t95.t2.t299 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t95.t2.t74))
% 3.65/3.91  (step t95.t2.t300 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule cong :premises (t95.t2.t26 t95.t2.t59))
% 3.65/3.91  (step t95.t2.t301 (cl (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule trans :premises (t95.t2.a4 t95.t2.t299 t95.t2.t300))
% 3.65/3.91  (step t95.t2.t302 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule cong :premises (t95.t2.t298 t95.t2.t301))
% 3.65/3.91  (step t95.t2.t303 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule symm :premises (t95.t2.a24))
% 3.65/3.91  (step t95.t2.t304 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule symm :premises (t95.t2.a23))
% 3.65/3.91  (step t95.t2.t305 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule cong :premises (t95.t2.a4 t95.t2.t79))
% 3.65/3.91  (step t95.t2.t306 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.inverse tptp.a))) :rule trans :premises (t95.t2.t295 t95.t2.t297 t95.t2.t302 t95.t2.t303 t95.t2.t304 t95.t2.t305 t95.t2.t74 t95.t2.t26))
% 3.65/3.91  (step t95.t2.t307 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t293 t95.t2.t306))
% 3.65/3.91  (step t95.t2.t308 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) :rule trans :premises (t95.t2.t276 t95.t2.t278 t95.t2.t307))
% 3.65/3.91  (step t95.t2.t309 (cl (= (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t95.t2.a66))
% 3.65/3.91  (step t95.t2.t310 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t309 t95.t2.t17))
% 3.65/3.91  (step t95.t2.t311 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule symm :premises (t95.t2.a65))
% 3.65/3.91  (step t95.t2.t312 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a64))
% 3.65/3.91  (step t95.t2.t313 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity) tptp.identity)) :rule trans :premises (t95.t2.t310 t95.t2.t311 t95.t2.t312 t95.t2.t15 t95.t2.t114))
% 3.65/3.91  (step t95.t2.t314 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule cong :premises (t95.t2.t308 t95.t2.t313))
% 3.65/3.91  (step t95.t2.t315 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.a2))
% 3.65/3.91  (step t95.t2.t316 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) tptp.identity)) :rule symm :premises (t95.t2.a1))
% 3.65/3.91  (step t95.t2.t317 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) tptp.identity)) :rule trans :premises (t95.t2.t314 t95.t2.t315 t95.t2.t316))
% 3.65/3.91  (step t95.t2.t318 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule symm :premises (t95.t2.a78))
% 3.65/3.91  (step t95.t2.t319 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule symm :premises (t95.t2.a77))
% 3.65/3.91  (step t95.t2.t320 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule symm :premises (t95.t2.t319))
% 3.65/3.91  (step t95.t2.t321 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a76))
% 3.65/3.91  (step t95.t2.t322 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t88 t95.t2.t3))
% 3.65/3.91  (step t95.t2.t323 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)))) :rule symm :premises (t95.t2.a75))
% 3.65/3.91  (step t95.t2.t324 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t323))
% 3.65/3.91  (step t95.t2.t325 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t89 t95.t2.t3))
% 3.65/3.91  (step t95.t2.t326 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) :rule trans :premises (t95.t2.t325 t95.t2.t53 t95.t2.t54))
% 3.65/3.91  (step t95.t2.t327 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.identity tptp.a))) :rule cong :premises (t95.t2.t52 t95.t2.t13))
% 3.65/3.91  (step t95.t2.t328 (cl (= (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t327))
% 3.65/3.91  (step t95.t2.t329 (cl (= (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t328 t95.t2.t3))
% 3.65/3.91  (step t95.t2.t330 (cl (= (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t19))
% 3.65/3.91  (step t95.t2.t331 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a tptp.identity))) :rule trans :premises (t95.t2.t327 t95.t2.t330 t95.t2.a31 t95.t2.t140))
% 3.65/3.91  (step t95.t2.t332 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t331 t95.t2.t3))
% 3.65/3.91  (step t95.t2.t333 (cl (= (tptp.multiply (tptp.multiply tptp.a tptp.identity) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) :rule cong :premises (t95.t2.t84 t95.t2.t3))
% 3.65/3.91  (step t95.t2.t334 (cl (= (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)) tptp.identity)) :rule trans :premises (t95.t2.t329 t95.t2.t332 t95.t2.t333 t95.t2.t15 t95.t2.t114))
% 3.65/3.91  (step t95.t2.t335 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule cong :premises (t95.t2.t326 t95.t2.t334))
% 3.65/3.91  (step t95.t2.t336 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) :rule trans :premises (t95.t2.t321 t95.t2.t322 t95.t2.t324 t95.t2.t335))
% 3.65/3.91  (step t95.t2.t337 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule cong :premises (t95.t2.t336 t95.t2.t97))
% 3.65/3.91  (step t95.t2.t338 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule symm :premises (t95.t2.a74))
% 3.65/3.91  (step t95.t2.t339 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule trans :premises (t95.t2.t318 t95.t2.t320 t95.t2.t337 t95.t2.t338))
% 3.65/3.91  (step t95.t2.t340 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule cong :premises (t95.t2.t61 t95.t2.t79))
% 3.65/3.91  (step t95.t2.t341 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule symm :premises (t95.t2.t340))
% 3.65/3.91  (step t95.t2.t342 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule symm :premises (t95.t2.t76))
% 3.65/3.91  (step t95.t2.t343 (cl (= (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule trans :premises (t95.t2.t57 t95.t2.t58 t95.t2.t342 t95.t2.a22))
% 3.65/3.91  (step t95.t2.t344 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule cong :premises (t95.t2.t97 t95.t2.t343))
% 3.65/3.91  (step t95.t2.t345 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t344))
% 3.65/3.91  (step t95.t2.t346 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule trans :premises (t95.t2.t341 t95.t2.t345))
% 3.65/3.91  (step t95.t2.t347 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) tptp.identity)) :rule symm :premises (t95.t2.a70))
% 3.65/3.91  (step t95.t2.t348 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.t347))
% 3.65/3.91  (step t95.t2.t349 (cl (= tptp.identity (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule trans :premises (t95.t2.a3 t95.t2.t285 t95.t2.a5))
% 3.65/3.91  (step t95.t2.t350 (cl (= (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule refl)
% 3.65/3.91  (step t95.t2.t351 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule cong :premises (t95.t2.t349 t95.t2.t350))
% 3.65/3.91  (step t95.t2.t352 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule symm :premises (t95.t2.a69))
% 3.65/3.91  (step t95.t2.t353 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule symm :premises (t95.t2.a68))
% 3.65/3.91  (step t95.t2.t354 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule symm :premises (t95.t2.t353))
% 3.65/3.91  (step t95.t2.t355 (cl (= tptp.identity (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule trans :premises (t95.t2.t348 t95.t2.t351 t95.t2.t352 t95.t2.t354))
% 3.65/3.91  (step t95.t2.t356 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule cong :premises (t95.t2.t346 t95.t2.t355))
% 3.65/3.91  (step t95.t2.t357 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule symm :premises (t95.t2.t356))
% 3.65/3.91  (step t95.t2.t358 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule symm :premises (t95.t2.a73))
% 3.65/3.91  (step t95.t2.t359 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule cong :premises (t95.t2.t20 t95.t2.t338))
% 3.65/3.91  (step t95.t2.t360 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule symm :premises (t95.t2.t359))
% 3.65/3.91  (step t95.t2.t361 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule trans :premises (t95.t2.t341 t95.t2.t345 t95.t2.a67 t95.t2.t357 t95.t2.t358 t95.t2.t360))
% 3.65/3.91  (step t95.t2.t362 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule symm :premises (t95.t2.t358))
% 3.65/3.91  (step t95.t2.t363 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule trans :premises (t95.t2.t339 t95.t2.t361 t95.t2.t359 t95.t2.t362))
% 3.65/3.91  (step t95.t2.t364 (cl (= (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)) tptp.identity)) :rule symm :premises (t95.t2.a79))
% 3.65/3.91  (step t95.t2.t365 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) :rule symm :premises (t95.t2.t364))
% 3.65/3.91  (step t95.t2.t366 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule cong :premises (t95.t2.t363 t95.t2.t365))
% 3.65/3.91  (step t95.t2.t367 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule symm :premises (t95.t2.a72))
% 3.65/3.91  (step t95.t2.t368 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule refl)
% 3.65/3.91  (step t95.t2.t369 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) tptp.identity)) :rule symm :premises (t95.t2.a71))
% 3.65/3.91  (step t95.t2.t370 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule cong :premises (t95.t2.t368 t95.t2.t369))
% 3.65/3.91  (step t95.t2.t371 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule symm :premises (t95.t2.a67))
% 3.65/3.91  (step t95.t2.t372 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule trans :premises (t95.t2.t366 t95.t2.t367 t95.t2.t370 t95.t2.t356 t95.t2.t371 t95.t2.t344 t95.t2.t340))
% 3.65/3.91  (step t95.t2.t373 (cl (= (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule cong :premises (t95.t2.t317 t95.t2.t372))
% 3.65/3.91  (step t95.t2.t374 (cl (= (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) false) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule equiv_simplify)
% 3.65/3.91  (step t95.t2.t375 (cl (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) false) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule equiv2 :premises (t95.t2.t374))
% 3.65/3.91  (step t95.t2.t376 (cl (not (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule not_not)
% 3.65/3.91  (step t95.t2.t377 (cl (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) false) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t95.t2.t375 t95.t2.t376))
% 3.65/3.91  (step t95.t2.t378 (cl (= (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) false)) :rule resolution :premises (t95.t2.t377 t95.t2.a0))
% 3.65/3.91  (step t95.t2.t379 (cl (= (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)) false)) :rule trans :premises (t95.t2.t373 t95.t2.t378))
% 3.65/3.91  (step t95.t2.t380 (cl (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule resolution :premises (t95.t2.t2 t95.t2.t379))
% 3.65/3.91  (step t95.t2 (cl (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (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.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule subproof :discharge (t95.t2.a0 t95.t2.a1 t95.t2.a2 t95.t2.a3 t95.t2.a4 t95.t2.a5 t95.t2.a6 t95.t2.a7 t95.t2.a8 t95.t2.a9 t95.t2.a10 t95.t2.a11 t95.t2.a12 t95.t2.a13 t95.t2.a14 t95.t2.a15 t95.t2.a16 t95.t2.a17 t95.t2.a18 t95.t2.a19 t95.t2.a20 t95.t2.a21 t95.t2.a22 t95.t2.a23 t95.t2.a24 t95.t2.a25 t95.t2.a26 t95.t2.a27 t95.t2.a28 t95.t2.a29 t95.t2.a30 t95.t2.a31 t95.t2.a32 t95.t2.a33 t95.t2.a34 t95.t2.a35 t95.t2.a36 t95.t2.a37 t95.t2.a38 t95.t2.a39 t95.t2.a40 t95.t2.a41 t95.t2.a42 t95.t2.a43 t95.t2.a44 t95.t2.a45 t95.t2.a46 t95.t2.a47 t95.t2.a48 t95.t2.a49 t95.t2.a50 t95.t2.a51 t95.t2.a52 t95.t2.a53 t95.t2.a54 t95.t2.a55 t95.t2.a56 t95.t2.a57 t95.t2.a58 t95.t2.a59 t95.t2.a60 t95.t2.a61 t95.t2.a62 t95.t2.a63 t95.t2.a64 t95.t2.a65 t95.t2.a66 t95.t2.a67 t95.t2.a68 t95.t2.a69 t95.t2.a70 t95.t2.a71 t95.t2.a72 t95.t2.a73 t95.t2.a74 t95.t2.a75 t95.t2.a76 t95.t2.a77 t95.t2.a78 t95.t2.a79))
% 3.65/3.91  (step t95.t3 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule and_pos)
% 3.65/3.91  (step t95.t4 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.91  (step t95.t5 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule and_pos)
% 3.65/3.91  (step t95.t6 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 3.65/3.91  (step t95.t7 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 3.65/3.91  (step t95.t8 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule and_pos)
% 3.65/3.91  (step t95.t9 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 3.65/3.91  (step t95.t10 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 3.65/3.92  (step t95.t11 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule and_pos)
% 3.65/3.92  (step t95.t12 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t13 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t14 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 3.65/3.92  (step t95.t15 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t16 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t17 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.inverse tptp.identity))) :rule and_pos)
% 3.65/3.92  (step t95.t18 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t19 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t20 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t21 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 3.65/3.92  (step t95.t22 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.65/3.92  (step t95.t23 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t24 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 3.65/3.92  (step t95.t25 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.65/3.92  (step t95.t26 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.65/3.92  (step t95.t27 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule and_pos)
% 3.65/3.92  (step t95.t28 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule and_pos)
% 3.65/3.92  (step t95.t29 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule and_pos)
% 3.65/3.92  (step t95.t30 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) :rule and_pos)
% 3.65/3.92  (step t95.t31 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t32 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t33 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t34 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule and_pos)
% 3.65/3.92  (step t95.t35 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 3.65/3.92  (step t95.t36 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t37 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t38 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule and_pos)
% 3.65/3.92  (step t95.t39 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.65/3.92  (step t95.t40 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule and_pos)
% 3.65/3.92  (step t95.t41 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t42 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t43 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.65/3.92  (step t95.t44 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule and_pos)
% 3.65/3.92  (step t95.t45 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t46 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t47 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t48 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t49 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t50 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t51 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t52 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) :rule and_pos)
% 3.65/3.92  (step t95.t53 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule and_pos)
% 3.65/3.92  (step t95.t54 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t55 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule and_pos)
% 3.65/3.92  (step t95.t56 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t57 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule and_pos)
% 3.65/3.92  (step t95.t58 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t59 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t60 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t61 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule and_pos)
% 3.65/3.92  (step t95.t62 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule and_pos)
% 3.65/3.92  (step t95.t63 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 3.65/3.92  (step t95.t64 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t65 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.65/3.92  (step t95.t66 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t67 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule and_pos)
% 3.65/3.93  (step t95.t68 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t69 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule and_pos)
% 3.65/3.93  (step t95.t70 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t71 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 3.65/3.93  (step t95.t72 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t73 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t74 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t75 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t76 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule and_pos)
% 3.65/3.93  (step t95.t77 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 3.65/3.93  (step t95.t78 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t79 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t80 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule and_pos)
% 3.65/3.93  (step t95.t81 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule and_pos)
% 3.65/3.93  (step t95.t82 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) :rule and_pos)
% 3.65/3.93  (step t95.t83 (cl (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule resolution :premises (t95.t2 t95.t3 t95.t4 t95.t5 t95.t6 t95.t7 t95.t8 t95.t9 t95.t10 t95.t11 t95.t12 t95.t13 t95.t14 t95.t15 t95.t16 t95.t17 t95.t18 t95.t19 t95.t20 t95.t21 t95.t22 t95.t23 t95.t24 t95.t25 t95.t26 t95.t27 t95.t28 t95.t29 t95.t30 t95.t31 t95.t32 t95.t33 t95.t34 t95.t35 t95.t36 t95.t37 t95.t38 t95.t39 t95.t40 t95.t41 t95.t42 t95.t43 t95.t44 t95.t45 t95.t46 t95.t47 t95.t48 t95.t49 t95.t50 t95.t51 t95.t52 t95.t53 t95.t54 t95.t55 t95.t56 t95.t57 t95.t58 t95.t59 t95.t60 t95.t61 t95.t62 t95.t63 t95.t64 t95.t65 t95.t66 t95.t67 t95.t68 t95.t69 t95.t70 t95.t71 t95.t72 t95.t73 t95.t74 t95.t75 t95.t76 t95.t77 t95.t78 t95.t79 t95.t80 t95.t81 t95.t82))
% 3.72/3.94  (step t95.t84 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule reordering :premises (t95.t83))
% 3.72/3.96  (step t95.t85 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule contraction :premises (t95.t84))
% 3.72/3.96  (step t95.t86 (cl (=> (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule resolution :premises (t95.t1 t95.t85))
% 3.72/3.96  (step t95.t87 (cl (=> (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule implies_neg2)
% 3.72/3.96  (step t95.t88 (cl (=> (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (=> (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule resolution :premises (t95.t86 t95.t87))
% 3.72/3.96  (step t95.t89 (cl (=> (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule contraction :premises (t95.t88))
% 3.72/3.96  (step t95.t90 (cl (not (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule implies :premises (t95.t89))
% 3.72/3.96  (step t95.t91 (cl (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (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.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule and_neg)
% 3.72/3.96  (step t95.t92 (cl (and (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.inverse tptp.identity)) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule resolution :premises (t95.t91 t95.a1 t95.a72 t95.a78 t95.a3 t95.a8 t95.a15 t95.a21 t95.a7 t95.a10 t95.a30 t95.a48 t95.a25 t95.a6 t95.a17 t95.a0 t95.a16 t95.a19 t95.a18 t95.a28 t95.a39 t95.a63 t95.a11 t95.a33 t95.a47 t95.a56 t95.a62 t95.a74 t95.a5 t95.a34 t95.a35 t95.a32 t95.a20 t95.a40 t95.a44 t95.a54 t95.a27 t95.a12 t95.a31 t95.a42 t95.a66 t95.a67 t95.a55 t95.a29 t95.a46 t95.a57 t95.a51 t95.a76 t95.a36 t95.a38 t95.a43 t95.a24 t95.a64 t95.a68 t95.a70 t95.a60 t95.a58 t95.a50 t95.a52 t95.a37 t95.a2 t95.a9 t95.a71 t95.a65 t95.a69 t95.a73 t95.a79 t95.a77 t95.a59 t95.a45 t95.a23 t95.a14 t95.a26 t95.a49 t95.a22 t95.a4 t95.a53 t95.a41 t95.a61 t95.a75 t95.a13))
% 3.72/3.96  (step t95.t93 (cl (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule resolution :premises (t95.t90 t95.t92))
% 3.72/3.96  (step t95 (cl (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule subproof :discharge (t95.a0 t95.a1 t95.a2 t95.a3 t95.a4 t95.a5 t95.a6 t95.a7 t95.a8 t95.a9 t95.a10 t95.a11 t95.a12 t95.a13 t95.a14 t95.a15 t95.a16 t95.a17 t95.a18 t95.a19 t95.a20 t95.a21 t95.a22 t95.a23 t95.a24 t95.a25 t95.a26 t95.a27 t95.a28 t95.a29 t95.a30 t95.a31 t95.a32 t95.a33 t95.a34 t95.a35 t95.a36 t95.a37 t95.a38 t95.a39 t95.a40 t95.a41 t95.a42 t95.a43 t95.a44 t95.a45 t95.a46 t95.a47 t95.a48 t95.a49 t95.a50 t95.a51 t95.a52 t95.a53 t95.a54 t95.a55 t95.a56 t95.a57 t95.a58 t95.a59 t95.a60 t95.a61 t95.a62 t95.a63 t95.a64 t95.a65 t95.a66 t95.a67 t95.a68 t95.a69 t95.a70 t95.a71 t95.a72 t95.a73 t95.a74 t95.a75 t95.a76 t95.a77 t95.a78 t95.a79))
% 3.72/3.96  (step t96 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.inverse tptp.identity))) :rule and_pos)
% 3.72/3.96  (step t97 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule and_pos)
% 3.72/3.96  (step t98 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule and_pos)
% 3.72/3.96  (step t99 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 3.72/3.96  (step t100 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 3.72/3.96  (step t101 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) :rule and_pos)
% 3.72/3.96  (step t102 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t103 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule and_pos)
% 3.72/3.96  (step t104 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 3.72/3.96  (step t105 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 3.72/3.96  (step t106 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule and_pos)
% 3.72/3.96  (step t107 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 3.72/3.96  (step t108 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.72/3.96  (step t109 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t110 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t111 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t112 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t113 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t114 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t115 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t116 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule and_pos)
% 3.72/3.96  (step t117 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t118 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule and_pos)
% 3.72/3.96  (step t119 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t120 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule and_pos)
% 3.72/3.96  (step t121 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 3.72/3.96  (step t122 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t123 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule and_pos)
% 3.72/3.96  (step t124 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule and_pos)
% 3.72/3.96  (step t125 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t126 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t127 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule and_pos)
% 3.72/3.96  (step t128 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t129 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.72/3.96  (step t130 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t131 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t132 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t133 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t134 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t135 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.72/3.96  (step t136 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule and_pos)
% 3.72/3.96  (step t137 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t138 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t139 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) :rule and_pos)
% 3.72/3.96  (step t140 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.96  (step t141 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 3.72/3.96  (step t142 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t143 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.72/3.97  (step t144 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 3.72/3.97  (step t145 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t146 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t147 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t148 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t149 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t150 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t151 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule and_pos)
% 3.72/3.97  (step t152 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule and_pos)
% 3.72/3.97  (step t153 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t154 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t155 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t156 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule and_pos)
% 3.72/3.97  (step t157 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule and_pos)
% 3.72/3.97  (step t158 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule and_pos)
% 3.72/3.97  (step t159 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 3.72/3.97  (step t160 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t161 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t162 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t163 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule and_pos)
% 3.72/3.97  (step t164 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule and_pos)
% 3.72/3.97  (step t165 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t166 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t167 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t168 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t169 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule and_pos)
% 3.72/3.97  (step t170 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule and_pos)
% 3.72/3.97  (step t171 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t172 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t173 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule and_pos)
% 3.72/3.97  (step t174 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule and_pos)
% 3.72/3.97  (step t175 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule and_pos)
% 3.72/3.97  (step t176 (cl (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule resolution :premises (t95 t96 t97 t98 t99 t100 t101 t102 t103 t104 t105 t106 t107 t108 t109 t110 t111 t112 t113 t114 t115 t116 t117 t118 t119 t120 t121 t122 t123 t124 t125 t126 t127 t128 t129 t130 t131 t132 t133 t134 t135 t136 t137 t138 t139 t140 t141 t142 t143 t144 t145 t146 t147 t148 t149 t150 t151 t152 t153 t154 t155 t156 t157 t158 t159 t160 t161 t162 t163 t164 t165 t166 t167 t168 t169 t170 t171 t172 t173 t174 t175))
% 3.73/3.98  (step t177 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule reordering :premises (t176))
% 3.73/3.99  (step t178 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule contraction :premises (t177))
% 3.73/3.99  (step t179 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule resolution :premises (t94 t178))
% 3.73/3.99  (step t180 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule implies_neg2)
% 3.73/3.99  (step t181 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule resolution :premises (t179 t180))
% 3.73/3.99  (step t182 (cl (=> (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule contraction :premises (t181))
% 3.73/3.99  (step t183 (cl (not (and (= tptp.identity (tptp.inverse tptp.identity)) (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule implies :premises (t182))
% 3.73/3.99  (step t184 (cl (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule resolution :premises (t93 t183))
% 3.73/3.99  (step t185 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.identity (tptp.inverse tptp.identity))))) :rule or_neg)
% 3.73/3.99  (step t186 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))))) :rule or_neg)
% 3.73/3.99  (step t187 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))))) :rule or_neg)
% 3.73/3.99  (step t188 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or_neg)
% 3.73/3.99  (step t189 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule or_neg)
% 3.73/4.00  (step t190 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))))) :rule or_neg)
% 3.73/4.00  (step t191 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t192 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule or_neg)
% 3.73/4.00  (step t193 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule or_neg)
% 3.73/4.00  (step t194 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))))) :rule or_neg)
% 3.73/4.00  (step t195 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))))) :rule or_neg)
% 3.73/4.00  (step t196 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule or_neg)
% 3.73/4.00  (step t197 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule or_neg)
% 3.73/4.00  (step t198 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t199 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t200 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t201 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t202 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t203 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t204 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t205 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))))) :rule or_neg)
% 3.73/4.00  (step t206 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t207 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))))) :rule or_neg)
% 3.73/4.00  (step t208 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t209 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))))) :rule or_neg)
% 3.73/4.00  (step t210 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))) :rule or_neg)
% 3.73/4.00  (step t211 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t212 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))))) :rule or_neg)
% 3.73/4.00  (step t213 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))))) :rule or_neg)
% 3.73/4.00  (step t214 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t215 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t216 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))))) :rule or_neg)
% 3.73/4.00  (step t217 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t218 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule or_neg)
% 3.73/4.00  (step t219 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t220 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t221 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t222 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t223 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t224 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule or_neg)
% 3.73/4.00  (step t225 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))))) :rule or_neg)
% 3.73/4.00  (step t226 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t227 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t228 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))))) :rule or_neg)
% 3.73/4.00  (step t229 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t230 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t231 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t232 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule or_neg)
% 3.73/4.00  (step t233 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t234 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t235 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t236 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t237 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t238 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t239 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t240 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))))) :rule or_neg)
% 3.73/4.00  (step t241 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))))) :rule or_neg)
% 3.73/4.00  (step t242 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t243 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t244 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t245 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))))) :rule or_neg)
% 3.73/4.00  (step t246 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t247 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))))) :rule or_neg)
% 3.73/4.00  (step t248 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or_neg)
% 3.73/4.00  (step t249 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t250 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t251 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.00  (step t252 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule or_neg)
% 3.73/4.01  (step t253 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))))) :rule or_neg)
% 3.73/4.01  (step t254 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.01  (step t255 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))))) :rule or_neg)
% 3.73/4.01  (step t256 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule or_neg)
% 3.73/4.01  (step t257 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.01  (step t258 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))) :rule or_neg)
% 3.73/4.01  (step t259 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))))) :rule or_neg)
% 3.73/4.01  (step t260 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))))) :rule or_neg)
% 3.73/4.01  (step t261 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.01  (step t262 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))) :rule or_neg)
% 3.73/4.01  (step t263 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))))) :rule or_neg)
% 3.73/4.01  (step t264 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))))) :rule or_neg)
% 3.73/4.01  (step t265 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (not (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule or_neg)
% 3.73/4.01  (step t266 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule resolution :premises (t184 t185 t186 t187 t188 t189 t190 t191 t192 t193 t194 t195 t196 t197 t198 t199 t200 t201 t202 t203 t204 t205 t206 t207 t208 t209 t210 t211 t212 t213 t214 t215 t216 t217 t218 t219 t220 t221 t222 t223 t224 t225 t226 t227 t228 t229 t230 t231 t232 t233 t234 t235 t236 t237 t238 t239 t240 t241 t242 t243 t244 t245 t246 t247 t248 t249 t250 t251 t252 t253 t254 t255 t256 t257 t258 t259 t260 t261 t262 t263 t264 t265))
% 3.73/4.02  (step t267 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (not (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule contraction :premises (t266))
% 3.73/4.02  (step t268 (cl (or (not (= tptp.identity (tptp.inverse tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))))) :rule resolution :premises (t1 t92 t267))
% 3.73/4.02  (step t269 (cl (not (= tptp.identity (tptp.inverse tptp.identity))) (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule or :premises (t268))
% 3.73/4.02  (step t270 (cl (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule reordering :premises (t269))
% 3.73/4.02  (step t271 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) (forall ((X $$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)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t272)
% 3.73/4.02  (assume t272.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 3.73/4.02  (step t272.t1 (cl (or (not (forall ((X $$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)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (:= Y (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) (:= Z tptp.identity)))
% 3.73/4.02  (step t272.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) :rule or :premises (t272.t1))
% 3.73/4.02  (step t272.t3 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) :rule resolution :premises (t272.t2 t272.a0))
% 3.73/4.02  (step t272 (cl (not (forall ((X $$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)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) :rule subproof :discharge (t272.a0))
% 3.73/4.02  (step t273 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) :rule resolution :premises (t271 t272))
% 3.73/4.02  (step t274 (cl (=> (forall ((X $$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))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule implies_neg2)
% 3.73/4.02  (step t275 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) (=> (forall ((X $$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))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule resolution :premises (t273 t274))
% 3.73/4.02  (step t276 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity)))) :rule contraction :premises (t275))
% 3.73/4.02  (step t277 (cl (not (forall ((X $$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)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) :rule implies :premises (t276))
% 3.73/4.02  (step t278 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))) tptp.identity))) :rule resolution :premises (t277 a6))
% 3.73/4.02  (step t279 (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.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t280)
% 3.73/4.02  (assume t280.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 3.73/4.02  (step t280.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.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.inverse tptp.a))) (:= Y (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))
% 3.73/4.02  (step t280.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.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule or :premises (t280.t1))
% 3.73/4.02  (step t280.t3 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t280.t2 t280.a0))
% 3.73/4.02  (step t280 (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.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule subproof :discharge (t280.a0))
% 3.73/4.02  (step t281 (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.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t279 t280))
% 3.73/4.02  (step t282 (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.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t283 (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.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (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.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule resolution :premises (t281 t282))
% 3.73/4.02  (step t284 (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.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule contraction :premises (t283))
% 3.73/4.02  (step t285 (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.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule implies :premises (t284))
% 3.73/4.02  (step t286 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t285 a4))
% 3.73/4.02  (step t287 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t288)
% 3.73/4.02  (assume t288.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 3.73/4.02  (step t288.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.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))))
% 3.73/4.02  (step t288.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.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule or :premises (t288.t1))
% 3.73/4.02  (step t288.t3 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule resolution :premises (t288.t2 t288.a0))
% 3.73/4.02  (step t288 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule subproof :discharge (t288.a0))
% 3.73/4.02  (step t289 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule resolution :premises (t287 t288))
% 3.73/4.02  (step t290 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))) :rule implies_neg2)
% 3.73/4.02  (step t291 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))) :rule resolution :premises (t289 t290))
% 3.73/4.02  (step t292 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity)))) :rule contraction :premises (t291))
% 3.73/4.02  (step t293 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule implies :premises (t292))
% 3.73/4.02  (step t294 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)) tptp.identity))) :rule resolution :premises (t293 a4))
% 3.73/4.02  (step t295 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t296)
% 3.73/4.02  (assume t296.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 3.73/4.02  (step t296.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))
% 3.73/4.02  (step t296.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule or :premises (t296.t1))
% 3.73/4.02  (step t296.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule resolution :premises (t296.t2 t296.a0))
% 3.73/4.02  (step t296 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule subproof :discharge (t296.a0))
% 3.73/4.02  (step t297 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule resolution :premises (t295 t296))
% 3.73/4.02  (step t298 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t299 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule resolution :premises (t297 t298))
% 3.73/4.02  (step t300 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule contraction :premises (t299))
% 3.73/4.02  (step t301 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule implies :premises (t300))
% 3.73/4.02  (step t302 (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)
% 3.73/4.02  (anchor :step t303 :args ((X $$unsorted) (:= X X)))
% 3.73/4.02  (step t303.t1 (cl (= X X)) :rule refl)
% 3.73/4.02  (step t303.t2 (cl (= (= (tptp.multiply tptp.identity X) X) (= X (tptp.multiply tptp.identity X)))) :rule all_simplify)
% 3.73/4.02  (step t303 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) :rule bind)
% 3.73/4.02  (step t304 (cl (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule resolution :premises (t302 t303 a0))
% 3.73/4.02  (step t305 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule resolution :premises (t301 t304))
% 3.73/4.02  (step t306 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (forall ((Y $$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)
% 3.73/4.02  (anchor :step t307)
% 3.73/4.02  (assume t307.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 3.73/4.02  (step t307.t1 (cl (or (not (forall ((Y $$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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= Y (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (:= Z (tptp.inverse (tptp.inverse tptp.a))) (:= X (tptp.inverse tptp.a))))
% 3.73/4.02  (step t307.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule or :premises (t307.t1))
% 3.73/4.02  (step t307.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t307.t2 t307.a0))
% 3.73/4.02  (step t307 (cl (not (forall ((Y $$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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule subproof :discharge (t307.a0))
% 3.73/4.02  (step t308 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t306 t307))
% 3.73/4.02  (step t309 (cl (=> (forall ((Y $$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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t310 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (=> (forall ((Y $$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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule resolution :premises (t308 t309))
% 3.73/4.02  (step t311 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule contraction :premises (t310))
% 3.73/4.02  (step t312 (cl (not (forall ((Y $$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.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies :premises (t311))
% 3.73/4.02  (step t313 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t312 a14))
% 3.73/4.02  (step t314 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (forall ((Y $$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)
% 3.73/4.02  (anchor :step t315)
% 3.73/4.02  (assume t315.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 3.73/4.02  (step t315.t1 (cl (or (not (forall ((Y $$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.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))) :rule forall_inst :args ((:= Y (tptp.inverse tptp.a)) (:= Z tptp.identity) (:= X (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))
% 3.73/4.02  (step t315.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule or :premises (t315.t1))
% 3.73/4.02  (step t315.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule resolution :premises (t315.t2 t315.a0))
% 3.73/4.02  (step t315 (cl (not (forall ((Y $$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.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule subproof :discharge (t315.a0))
% 3.73/4.02  (step t316 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule resolution :premises (t314 t315))
% 3.73/4.02  (step t317 (cl (=> (forall ((Y $$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.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t318 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) (=> (forall ((Y $$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.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))) :rule resolution :premises (t316 t317))
% 3.73/4.02  (step t319 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))))) :rule contraction :premises (t318))
% 3.73/4.02  (step t320 (cl (not (forall ((Y $$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.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule implies :premises (t319))
% 3.73/4.02  (step t321 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule resolution :premises (t320 a13))
% 3.73/4.02  (step t322 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (forall ((X $$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)
% 3.73/4.02  (anchor :step t323)
% 3.73/4.02  (assume t323.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 3.73/4.02  (step t323.t1 (cl (or (not (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (:= Z (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))
% 3.73/4.02  (step t323.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.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule or :premises (t323.t1))
% 3.73/4.02  (step t323.t3 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule resolution :premises (t323.t2 t323.a0))
% 3.73/4.02  (step t323 (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.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule subproof :discharge (t323.a0))
% 3.73/4.02  (step t324 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule resolution :premises (t322 t323))
% 3.73/4.02  (step t325 (cl (=> (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))))) :rule implies_neg2)
% 3.73/4.02  (step t326 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) (=> (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))))) :rule resolution :premises (t324 t325))
% 3.73/4.02  (step t327 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))))) :rule contraction :premises (t326))
% 3.73/4.02  (step t328 (cl (not (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule implies :premises (t327))
% 3.73/4.02  (step t329 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule resolution :premises (t328 a12))
% 3.73/4.02  (step t330 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t331)
% 3.73/4.02  (assume t331.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 3.73/4.02  (step t331.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.inverse tptp.a))) (:= Y tptp.a)))
% 3.73/4.02  (step t331.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule or :premises (t331.t1))
% 3.73/4.02  (step t331.t3 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule resolution :premises (t331.t2 t331.a0))
% 3.73/4.02  (step t331 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule subproof :discharge (t331.a0))
% 3.73/4.02  (step t332 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule resolution :premises (t330 t331))
% 3.73/4.02  (step t333 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t334 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule resolution :premises (t332 t333))
% 3.73/4.02  (step t335 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a))))) :rule contraction :premises (t334))
% 3.73/4.02  (step t336 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule implies :premises (t335))
% 3.73/4.02  (step t337 (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)
% 3.73/4.02  (anchor :step t338 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 3.73/4.02  (step t338.t1 (cl (= X X)) :rule refl)
% 3.73/4.02  (step t338.t2 (cl (= Y Y)) :rule refl)
% 3.73/4.02  (step t338.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)
% 3.73/4.02  (step t338 (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)
% 3.73/4.02  (step t339 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule resolution :premises (t337 t338 a9))
% 3.73/4.02  (step t340 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)))) :rule resolution :premises (t336 t339))
% 3.73/4.02  (step t341 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t342)
% 3.73/4.02  (assume t342.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 3.73/4.02  (step t342.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.inverse tptp.a))))
% 3.73/4.02  (step t342.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) :rule or :premises (t342.t1))
% 3.73/4.02  (step t342.t3 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t342.t2 t342.a0))
% 3.73/4.02  (step t342 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) :rule subproof :discharge (t342.a0))
% 3.73/4.02  (step t343 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t341 t342))
% 3.73/4.02  (step t344 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t345 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))))) :rule resolution :premises (t343 t344))
% 3.73/4.02  (step t346 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a)))))) :rule contraction :premises (t345))
% 3.73/4.02  (step t347 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) :rule implies :premises (t346))
% 3.73/4.02  (step t348 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t347 t339))
% 3.73/4.02  (step t349 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (forall ((X $$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)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t350)
% 3.73/4.02  (assume t350.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))))
% 3.73/4.02  (step t350.t1 (cl (or (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (:= Y (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (:= Z (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.73/4.02  (step t350.t2 (cl (not (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)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or :premises (t350.t1))
% 3.73/4.02  (step t350.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t350.t2 t350.a0))
% 3.73/4.02  (step t350 (cl (not (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)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule subproof :discharge (t350.a0))
% 3.73/4.02  (step t351 (cl (=> (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))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t349 t350))
% 3.73/4.02  (step t352 (cl (=> (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))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t353 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule resolution :premises (t351 t352))
% 3.73/4.02  (step t354 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule contraction :premises (t353))
% 3.73/4.02  (step t355 (cl (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies :premises (t354))
% 3.73/4.02  (step t356 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t355 a5))
% 3.73/4.02  (step t357 (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.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t358)
% 3.73/4.02  (assume t358.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 3.73/4.02  (step t358.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.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))) (:= Y (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.73/4.02  (step t358.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.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule or :premises (t358.t1))
% 3.73/4.02  (step t358.t3 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t358.t2 t358.a0))
% 3.73/4.02  (step t358 (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.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule subproof :discharge (t358.a0))
% 3.73/4.02  (step t359 (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.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t357 t358))
% 3.73/4.02  (step t360 (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.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t361 (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.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule resolution :premises (t359 t360))
% 3.73/4.02  (step t362 (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.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule contraction :premises (t361))
% 3.73/4.02  (step t363 (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.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule implies :premises (t362))
% 3.73/4.02  (step t364 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t363 a4))
% 3.73/4.02  (step t365 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t366)
% 3.73/4.02  (assume t366.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 3.73/4.02  (step t366.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.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.inverse tptp.a))) (:= Y tptp.a)))
% 3.73/4.02  (step t366.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.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule or :premises (t366.t1))
% 3.73/4.02  (step t366.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t366.t2 t366.a0))
% 3.73/4.02  (step t366 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule subproof :discharge (t366.a0))
% 3.73/4.02  (step t367 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t365 t366))
% 3.73/4.02  (step t368 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t369 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (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.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule resolution :premises (t367 t368))
% 3.73/4.02  (step t370 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule contraction :premises (t369))
% 3.73/4.02  (step t371 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule implies :premises (t370))
% 3.73/4.02  (step t372 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t371 a3))
% 3.73/4.02  (step t373 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t374)
% 3.73/4.02  (assume t374.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t374.t1 (cl (or (not (forall ((X $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (:= Y (tptp.inverse tptp.a)) (:= Z (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))
% 3.73/4.02  (step t374.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule or :premises (t374.t1))
% 3.73/4.02  (step t374.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule resolution :premises (t374.t2 t374.a0))
% 3.73/4.02  (step t374 (cl (not (forall ((X $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule subproof :discharge (t374.a0))
% 3.73/4.02  (step t375 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule resolution :premises (t373 t374))
% 3.73/4.02  (step t376 (cl (=> (forall ((X $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))))) :rule implies_neg2)
% 3.73/4.02  (step t377 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) (=> (forall ((X $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))))) :rule resolution :premises (t375 t376))
% 3.73/4.02  (step t378 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))))) :rule contraction :premises (t377))
% 3.73/4.02  (step t379 (cl (not (forall ((X $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule implies :premises (t378))
% 3.73/4.02  (step t380 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule resolution :premises (t379 a2))
% 3.73/4.02  (step t381 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t382)
% 3.73/4.02  (assume t382.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 3.73/4.02  (step t382.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.73/4.02  (step t382.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule or :premises (t382.t1))
% 3.73/4.02  (step t382.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t382.t2 t382.a0))
% 3.73/4.02  (step t382 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule subproof :discharge (t382.a0))
% 3.73/4.02  (step t383 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t381 t382))
% 3.73/4.02  (step t384 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 3.73/4.02  (step t385 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t383 t384))
% 3.73/4.02  (step t386 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule contraction :premises (t385))
% 3.73/4.02  (step t387 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies :premises (t386))
% 3.73/4.02  (step t388 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t387 t304))
% 3.73/4.02  (step t389 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (forall ((Y $$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)
% 3.73/4.02  (anchor :step t390)
% 3.73/4.02  (assume t390.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 3.73/4.02  (step t390.t1 (cl (or (not (forall ((Y $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= Y (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (:= Z (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (:= X (tptp.inverse tptp.a))))
% 3.73/4.02  (step t390.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule or :premises (t390.t1))
% 3.73/4.02  (step t390.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule resolution :premises (t390.t2 t390.a0))
% 3.73/4.02  (step t390 (cl (not (forall ((Y $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule subproof :discharge (t390.a0))
% 3.73/4.02  (step t391 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule resolution :premises (t389 t390))
% 3.73/4.02  (step t392 (cl (=> (forall ((Y $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t393 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (=> (forall ((Y $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule resolution :premises (t391 t392))
% 3.73/4.02  (step t394 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule contraction :premises (t393))
% 3.73/4.02  (step t395 (cl (not (forall ((Y $$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.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule implies :premises (t394))
% 3.73/4.02  (step t396 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule resolution :premises (t395 a14))
% 3.73/4.02  (step t397 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (forall ((Y $$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)
% 3.73/4.02  (anchor :step t398)
% 3.73/4.02  (assume t398.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 3.73/4.02  (step t398.t1 (cl (or (not (forall ((Y $$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.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule forall_inst :args ((:= Y (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (:= Z (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (:= X (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.73/4.02  (step t398.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule or :premises (t398.t1))
% 3.73/4.02  (step t398.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t398.t2 t398.a0))
% 3.73/4.02  (step t398 (cl (not (forall ((Y $$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.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule subproof :discharge (t398.a0))
% 3.73/4.02  (step t399 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t397 t398))
% 3.73/4.02  (step t400 (cl (=> (forall ((Y $$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.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t401 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (=> (forall ((Y $$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.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule resolution :premises (t399 t400))
% 3.73/4.02  (step t402 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule contraction :premises (t401))
% 3.73/4.02  (step t403 (cl (not (forall ((Y $$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.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies :premises (t402))
% 3.73/4.02  (step t404 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t403 a14))
% 3.73/4.02  (step t405 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (forall ((Y $$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)
% 3.73/4.02  (anchor :step t406)
% 3.73/4.02  (assume t406.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 3.73/4.02  (step t406.t1 (cl (or (not (forall ((Y $$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.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= Y (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (:= Z (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (:= X (tptp.inverse tptp.a))))
% 3.73/4.02  (step t406.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule or :premises (t406.t1))
% 3.73/4.02  (step t406.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule resolution :premises (t406.t2 t406.a0))
% 3.73/4.02  (step t406 (cl (not (forall ((Y $$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.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule subproof :discharge (t406.a0))
% 3.73/4.02  (step t407 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule resolution :premises (t405 t406))
% 3.73/4.02  (step t408 (cl (=> (forall ((Y $$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.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t409 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (=> (forall ((Y $$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.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule resolution :premises (t407 t408))
% 3.73/4.02  (step t410 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule contraction :premises (t409))
% 3.73/4.02  (step t411 (cl (not (forall ((Y $$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.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule implies :premises (t410))
% 3.73/4.02  (step t412 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule resolution :premises (t411 a13))
% 3.73/4.02  (step t413 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((X $$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)
% 3.73/4.02  (anchor :step t414)
% 3.73/4.02  (assume t414.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 3.73/4.02  (step t414.t1 (cl (or (not (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (:= Z tptp.a)))
% 3.73/4.02  (step t414.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t414.t1))
% 3.73/4.02  (step t414.t3 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t414.t2 t414.a0))
% 3.73/4.02  (step t414 (cl (not (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t414.a0))
% 3.73/4.02  (step t415 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t413 t414))
% 3.73/4.02  (step t416 (cl (=> (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t417 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t415 t416))
% 3.73/4.02  (step t418 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t417))
% 3.73/4.02  (step t419 (cl (not (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t418))
% 3.73/4.02  (step t420 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t419 a12))
% 3.73/4.02  (step t421 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (forall ((X $$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)
% 3.73/4.02  (anchor :step t422)
% 3.73/4.02  (assume t422.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 3.73/4.02  (step t422.t1 (cl (or (not (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (:= Z (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 3.73/4.02  (step t422.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule or :premises (t422.t1))
% 3.73/4.02  (step t422.t3 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule resolution :premises (t422.t2 t422.a0))
% 3.73/4.02  (step t422 (cl (not (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule subproof :discharge (t422.a0))
% 3.73/4.02  (step t423 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule resolution :premises (t421 t422))
% 3.73/4.02  (step t424 (cl (=> (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule implies_neg2)
% 3.73/4.02  (step t425 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) (=> (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule resolution :premises (t423 t424))
% 3.73/4.02  (step t426 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))))) :rule contraction :premises (t425))
% 3.73/4.02  (step t427 (cl (not (forall ((X $$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.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule implies :premises (t426))
% 3.73/4.02  (step t428 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule resolution :premises (t427 a12))
% 3.73/4.02  (step t429 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (forall ((X $$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)
% 3.73/4.02  (anchor :step t430)
% 3.73/4.02  (assume t430.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 3.73/4.02  (step t430.t1 (cl (or (not (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= Y (tptp.multiply tptp.a (tptp.inverse tptp.a))) (:= Z tptp.a)))
% 3.73/4.02  (step t430.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule or :premises (t430.t1))
% 3.73/4.02  (step t430.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t430.t2 t430.a0))
% 3.73/4.02  (step t430 (cl (not (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule subproof :discharge (t430.a0))
% 3.73/4.02  (step t431 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t429 t430))
% 3.73/4.02  (step t432 (cl (=> (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t433 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (=> (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t431 t432))
% 3.73/4.02  (step t434 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule contraction :premises (t433))
% 3.73/4.02  (step t435 (cl (not (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule implies :premises (t434))
% 3.73/4.02  (step t436 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.inverse tptp.a)) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t435 a12))
% 3.73/4.02  (step t437 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t438)
% 3.73/4.02  (assume t438.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 3.73/4.02  (step t438.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (:= Y (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.73/4.02  (step t438.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule or :premises (t438.t1))
% 3.73/4.02  (step t438.t3 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule resolution :premises (t438.t2 t438.a0))
% 3.73/4.02  (step t438 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule subproof :discharge (t438.a0))
% 3.73/4.02  (step t439 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule resolution :premises (t437 t438))
% 3.73/4.02  (step t440 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule implies_neg2)
% 3.73/4.02  (step t441 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule resolution :premises (t439 t440))
% 3.73/4.02  (step t442 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))))) :rule contraction :premises (t441))
% 3.73/4.02  (step t443 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule implies :premises (t442))
% 3.73/4.02  (step t444 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule resolution :premises (t443 t339))
% 3.73/4.02  (step t445 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t446)
% 3.73/4.02  (assume t446.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 3.73/4.02  (step t446.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (:= Y (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.73/4.02  (step t446.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or :premises (t446.t1))
% 3.73/4.02  (step t446.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t446.t2 t446.a0))
% 3.73/4.02  (step t446 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule subproof :discharge (t446.a0))
% 3.73/4.02  (step t447 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t445 t446))
% 3.73/4.02  (step t448 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t449 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule resolution :premises (t447 t448))
% 3.73/4.02  (step t450 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule contraction :premises (t449))
% 3.73/4.02  (step t451 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies :premises (t450))
% 3.73/4.02  (step t452 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t451 t339))
% 3.73/4.02  (step t453 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (forall ((X $$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)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t454)
% 3.73/4.02  (assume t454.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 3.73/4.02  (step t454.t1 (cl (or (not (forall ((X $$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)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (:= Y (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (:= Z (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))
% 3.73/4.02  (step t454.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule or :premises (t454.t1))
% 3.73/4.02  (step t454.t3 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t454.t2 t454.a0))
% 3.73/4.02  (step t454 (cl (not (forall ((X $$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)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule subproof :discharge (t454.a0))
% 3.73/4.02  (step t455 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t453 t454))
% 3.73/4.02  (step t456 (cl (=> (forall ((X $$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))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t457 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (=> (forall ((X $$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))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule resolution :premises (t455 t456))
% 3.73/4.02  (step t458 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule contraction :premises (t457))
% 3.73/4.02  (step t459 (cl (not (forall ((X $$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)))) (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule implies :premises (t458))
% 3.73/4.02  (step t460 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t459 a6))
% 3.73/4.02  (step t461 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (forall ((X $$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)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t462)
% 3.73/4.02  (assume t462.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))))
% 3.73/4.02  (step t462.t1 (cl (or (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (:= Y (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (:= Z (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))
% 3.73/4.02  (step t462.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or :premises (t462.t1))
% 3.73/4.02  (step t462.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t462.t2 t462.a0))
% 3.73/4.02  (step t462 (cl (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule subproof :discharge (t462.a0))
% 3.73/4.02  (step t463 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t461 t462))
% 3.73/4.02  (step t464 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t465 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule resolution :premises (t463 t464))
% 3.73/4.02  (step t466 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule contraction :premises (t465))
% 3.73/4.02  (step t467 (cl (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies :premises (t466))
% 3.73/4.02  (step t468 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t467 a5))
% 3.73/4.02  (step t469 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t470)
% 3.73/4.02  (assume t470.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 3.73/4.02  (step t470.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.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))) (:= Y (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.73/4.02  (step t470.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.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule or :premises (t470.t1))
% 3.73/4.02  (step t470.t3 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t470.t2 t470.a0))
% 3.73/4.02  (step t470 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule subproof :discharge (t470.a0))
% 3.73/4.02  (step t471 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t469 t470))
% 3.73/4.02  (step t472 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule implies_neg2)
% 3.73/4.02  (step t473 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule resolution :premises (t471 t472))
% 3.73/4.02  (step t474 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule contraction :premises (t473))
% 3.73/4.02  (step t475 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies :premises (t474))
% 3.73/4.02  (step t476 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.greatest_lower_bound (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t475 a3))
% 3.73/4.02  (step t477 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t478)
% 3.73/4.02  (assume t478.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t478.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.inverse tptp.a)) (:= Z (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.73/4.02  (step t478.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule or :premises (t478.t1))
% 3.73/4.02  (step t478.t3 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t478.t2 t478.a0))
% 3.73/4.02  (step t478 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule subproof :discharge (t478.a0))
% 3.73/4.02  (step t479 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t477 t478))
% 3.73/4.02  (step t480 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule implies_neg2)
% 3.73/4.02  (step t481 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule resolution :premises (t479 t480))
% 3.73/4.02  (step t482 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule contraction :premises (t481))
% 3.73/4.02  (step t483 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies :premises (t482))
% 3.73/4.02  (step t484 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t483 a2))
% 3.73/4.02  (step t485 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t486)
% 3.73/4.02  (assume t486.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t486.t1 (cl (or (not (forall ((X $$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.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.identity)) (:= Y (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (:= Z (tptp.inverse tptp.a))))
% 3.73/4.02  (step t486.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule or :premises (t486.t1))
% 3.73/4.02  (step t486.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule resolution :premises (t486.t2 t486.a0))
% 3.73/4.02  (step t486 (cl (not (forall ((X $$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.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule subproof :discharge (t486.a0))
% 3.73/4.02  (step t487 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule resolution :premises (t485 t486))
% 3.73/4.02  (step t488 (cl (=> (forall ((X $$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.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t489 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) (=> (forall ((X $$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.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule resolution :premises (t487 t488))
% 3.73/4.02  (step t490 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)))))) :rule contraction :premises (t489))
% 3.73/4.02  (step t491 (cl (not (forall ((X $$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.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule implies :premises (t490))
% 3.73/4.02  (step t492 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a)))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a))))) :rule resolution :premises (t491 a2))
% 3.73/4.02  (step t493 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (forall ((Y $$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)
% 3.73/4.02  (anchor :step t494)
% 3.73/4.02  (assume t494.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 3.73/4.02  (step t494.t1 (cl (or (not (forall ((Y $$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.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= Y (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (:= Z (tptp.multiply tptp.identity tptp.a)) (:= X (tptp.inverse tptp.a))))
% 3.73/4.02  (step t494.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) :rule or :premises (t494.t1))
% 3.73/4.02  (step t494.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) :rule resolution :premises (t494.t2 t494.a0))
% 3.73/4.02  (step t494 (cl (not (forall ((Y $$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.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) :rule subproof :discharge (t494.a0))
% 3.73/4.02  (step t495 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) :rule resolution :premises (t493 t494))
% 3.73/4.02  (step t496 (cl (=> (forall ((Y $$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.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t497 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) (=> (forall ((Y $$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.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))))) :rule resolution :premises (t495 t496))
% 3.73/4.02  (step t498 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a)))))) :rule contraction :premises (t497))
% 3.73/4.02  (step t499 (cl (not (forall ((Y $$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.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) :rule implies :premises (t498))
% 3.73/4.02  (step t500 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply tptp.identity tptp.a) (tptp.inverse tptp.a))))) :rule resolution :premises (t499 a13))
% 3.73/4.02  (step t501 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (forall ((Y $$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)
% 3.73/4.02  (anchor :step t502)
% 3.73/4.02  (assume t502.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 3.73/4.02  (step t502.t1 (cl (or (not (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (:= X (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.73/4.02  (step t502.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule or :premises (t502.t1))
% 3.73/4.02  (step t502.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t502.t2 t502.a0))
% 3.73/4.02  (step t502 (cl (not (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule subproof :discharge (t502.a0))
% 3.73/4.02  (step t503 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t501 t502))
% 3.73/4.02  (step t504 (cl (=> (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t505 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (=> (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule resolution :premises (t503 t504))
% 3.73/4.02  (step t506 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule contraction :premises (t505))
% 3.73/4.02  (step t507 (cl (not (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies :premises (t506))
% 3.73/4.02  (step t508 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t507 a13))
% 3.73/4.02  (step t509 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (forall ((X $$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)
% 3.73/4.02  (anchor :step t510)
% 3.73/4.02  (assume t510.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 3.73/4.02  (step t510.t1 (cl (or (not (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (:= Z (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.73/4.02  (step t510.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule or :premises (t510.t1))
% 3.73/4.02  (step t510.t3 (cl (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t510.t2 t510.a0))
% 3.73/4.02  (step t510 (cl (not (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule subproof :discharge (t510.a0))
% 3.73/4.02  (step t511 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t509 t510))
% 3.73/4.02  (step t512 (cl (=> (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t513 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (=> (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule resolution :premises (t511 t512))
% 3.73/4.02  (step t514 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule contraction :premises (t513))
% 3.73/4.02  (step t515 (cl (not (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies :premises (t514))
% 3.73/4.02  (step t516 (cl (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t515 a12))
% 3.73/4.02  (step t517 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (forall ((X $$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)
% 3.73/4.02  (anchor :step t518)
% 3.73/4.02  (assume t518.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 3.73/4.02  (step t518.t1 (cl (or (not (forall ((X $$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.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (:= Z (tptp.multiply tptp.identity tptp.a))))
% 3.73/4.02  (step t518.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule or :premises (t518.t1))
% 3.73/4.02  (step t518.t3 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t518.t2 t518.a0))
% 3.73/4.02  (step t518 (cl (not (forall ((X $$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.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule subproof :discharge (t518.a0))
% 3.73/4.02  (step t519 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t517 t518))
% 3.73/4.02  (step t520 (cl (=> (forall ((X $$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.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t521 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) (=> (forall ((X $$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.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule resolution :premises (t519 t520))
% 3.73/4.02  (step t522 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a)))))) :rule contraction :premises (t521))
% 3.73/4.02  (step t523 (cl (not (forall ((X $$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.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule implies :premises (t522))
% 3.73/4.02  (step t524 (cl (= (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t523 a11))
% 3.73/4.02  (step t525 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (forall ((X $$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)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t526)
% 3.73/4.02  (assume t526.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 3.73/4.02  (step t526.t1 (cl (or (not (forall ((X $$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)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (:= Y tptp.identity) (:= Z (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))
% 3.73/4.02  (step t526.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule or :premises (t526.t1))
% 3.73/4.02  (step t526.t3 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule resolution :premises (t526.t2 t526.a0))
% 3.73/4.02  (step t526 (cl (not (forall ((X $$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)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule subproof :discharge (t526.a0))
% 3.73/4.02  (step t527 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule resolution :premises (t525 t526))
% 3.73/4.02  (step t528 (cl (=> (forall ((X $$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))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t529 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (=> (forall ((X $$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))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule resolution :premises (t527 t528))
% 3.73/4.02  (step t530 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule contraction :premises (t529))
% 3.73/4.02  (step t531 (cl (not (forall ((X $$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)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule implies :premises (t530))
% 3.73/4.02  (step t532 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (tptp.least_upper_bound (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity) (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule resolution :premises (t531 a6))
% 3.73/4.02  (step t533 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((X $$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)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t534)
% 3.73/4.02  (assume t534.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))))
% 3.73/4.02  (step t534.t1 (cl (or (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))) (:= Y (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (:= Z (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 3.73/4.02  (step t534.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t534.t1))
% 3.73/4.02  (step t534.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t534.t2 t534.a0))
% 3.73/4.02  (step t534 (cl (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t534.a0))
% 3.73/4.02  (step t535 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t533 t534))
% 3.73/4.02  (step t536 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t537 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t535 t536))
% 3.73/4.02  (step t538 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t537))
% 3.73/4.02  (step t539 (cl (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t538))
% 3.73/4.02  (step t540 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t539 a5))
% 3.73/4.02  (step t541 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (forall ((X $$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)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t542)
% 3.73/4.02  (assume t542.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))))
% 3.73/4.02  (step t542.t1 (cl (or (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (:= Z (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.73/4.02  (step t542.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule or :premises (t542.t1))
% 3.73/4.02  (step t542.t3 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t542.t2 t542.a0))
% 3.73/4.02  (step t542 (cl (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule subproof :discharge (t542.a0))
% 3.73/4.02  (step t543 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t541 t542))
% 3.73/4.02  (step t544 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 3.73/4.02  (step t545 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t543 t544))
% 3.73/4.02  (step t546 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule contraction :premises (t545))
% 3.73/4.02  (step t547 (cl (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies :premises (t546))
% 3.73/4.02  (step t548 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity))) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t547 a5))
% 3.73/4.02  (step t549 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t550)
% 3.73/4.02  (assume t550.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 3.73/4.02  (step t550.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.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (:= Y (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))
% 3.73/4.02  (step t550.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.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule or :premises (t550.t1))
% 3.73/4.02  (step t550.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t550.t2 t550.a0))
% 3.73/4.02  (step t550 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule subproof :discharge (t550.a0))
% 3.73/4.02  (step t551 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t549 t550))
% 3.73/4.02  (step t552 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t553 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule resolution :premises (t551 t552))
% 3.73/4.02  (step t554 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)))))) :rule contraction :premises (t553))
% 3.73/4.02  (step t555 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies :premises (t554))
% 3.73/4.02  (step t556 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t555 a3))
% 3.73/4.02  (step t557 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t558)
% 3.73/4.02  (assume t558.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 3.73/4.02  (step t558.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.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (:= Y (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))))
% 3.73/4.02  (step t558.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.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t558.t1))
% 3.73/4.02  (step t558.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t558.t2 t558.a0))
% 3.73/4.02  (step t558 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t558.a0))
% 3.73/4.02  (step t559 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t557 t558))
% 3.73/4.02  (step t560 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t561 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t559 t560))
% 3.73/4.02  (step t562 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t561))
% 3.73/4.02  (step t563 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t562))
% 3.73/4.02  (step t564 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t563 a3))
% 3.73/4.02  (step t565 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t566)
% 3.73/4.02  (assume t566.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t566.t1 (cl (or (not (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (:= Y (tptp.inverse (tptp.inverse tptp.a))) (:= Z (tptp.inverse tptp.a))))
% 3.73/4.02  (step t566.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule or :premises (t566.t1))
% 3.73/4.02  (step t566.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t566.t2 t566.a0))
% 3.73/4.02  (step t566 (cl (not (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule subproof :discharge (t566.a0))
% 3.73/4.02  (step t567 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t565 t566))
% 3.73/4.02  (step t568 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t569 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (=> (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule resolution :premises (t567 t568))
% 3.73/4.02  (step t570 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule contraction :premises (t569))
% 3.73/4.02  (step t571 (cl (not (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies :premises (t570))
% 3.73/4.02  (step t572 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t571 a2))
% 3.73/4.02  (step t573 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)))) :rule equiv_pos2)
% 3.73/4.02  (step t574 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))) :rule refl)
% 3.73/4.02  (step t575 (cl (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)))) :rule all_simplify)
% 3.73/4.02  (step t576 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))))) :rule cong :premises (t574 t575))
% 3.73/4.02  (step t577 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t578)
% 3.73/4.02  (assume t578.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t578.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= Z tptp.a)))
% 3.73/4.02  (step t578.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule or :premises (t578.t1))
% 3.73/4.02  (step t578.t3 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t578.t2 t578.a0))
% 3.73/4.02  (step t578 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule subproof :discharge (t578.a0))
% 3.73/4.02  (step t579 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t577 t578))
% 3.73/4.02  (step t580 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t581 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t579 t580))
% 3.73/4.02  (step t582 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule contraction :premises (t581))
% 3.73/4.02  (step t583 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a)))) :rule resolution :premises (t573 t576 t582))
% 3.73/4.02  (step t584 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) :rule implies :premises (t583))
% 3.73/4.02  (step t585 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a))) :rule resolution :premises (t584 a2))
% 3.73/4.02  (step t586 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t587)
% 3.73/4.02  (assume t587.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t587.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.inverse (tptp.inverse tptp.a))) (:= Z (tptp.inverse tptp.a))))
% 3.73/4.02  (step t587.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule or :premises (t587.t1))
% 3.73/4.02  (step t587.t3 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t587.t2 t587.a0))
% 3.73/4.02  (step t587 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule subproof :discharge (t587.a0))
% 3.73/4.02  (step t588 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t586 t587))
% 3.73/4.02  (step t589 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t590 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule resolution :premises (t588 t589))
% 3.73/4.02  (step t591 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule contraction :premises (t590))
% 3.73/4.02  (step t592 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies :premises (t591))
% 3.73/4.02  (step t593 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t592 a2))
% 3.73/4.02  (step t594 (cl (=> (forall ((X $$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.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t595)
% 3.73/4.02  (assume t595.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t595.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= Y tptp.a) (:= Z (tptp.inverse tptp.a))))
% 3.73/4.02  (step t595.t2 (cl (not (forall ((X $$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.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule or :premises (t595.t1))
% 3.73/4.02  (step t595.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t595.t2 t595.a0))
% 3.73/4.02  (step t595 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule subproof :discharge (t595.a0))
% 3.73/4.02  (step t596 (cl (=> (forall ((X $$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.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t594 t595))
% 3.73/4.02  (step t597 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t598 (cl (=> (forall ((X $$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.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule resolution :premises (t596 t597))
% 3.73/4.02  (step t599 (cl (=> (forall ((X $$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.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a)))))) :rule contraction :premises (t598))
% 3.73/4.02  (step t600 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule implies :premises (t599))
% 3.73/4.02  (step t601 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a (tptp.inverse tptp.a))))) :rule resolution :premises (t600 a2))
% 3.73/4.02  (step t602 (cl (=> (forall ((X $$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.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t603)
% 3.73/4.02  (assume t603.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t603.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= Y tptp.a) (:= Z tptp.identity)))
% 3.73/4.02  (step t603.t2 (cl (not (forall ((X $$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.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule or :premises (t603.t1))
% 3.73/4.02  (step t603.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t603.t2 t603.a0))
% 3.73/4.02  (step t603 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule subproof :discharge (t603.a0))
% 3.73/4.02  (step t604 (cl (=> (forall ((X $$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.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t602 t603))
% 3.73/4.02  (step t605 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))))) :rule implies_neg2)
% 3.73/4.02  (step t606 (cl (=> (forall ((X $$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.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))))) :rule resolution :premises (t604 t605))
% 3.73/4.02  (step t607 (cl (=> (forall ((X $$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.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity))))) :rule contraction :premises (t606))
% 3.73/4.02  (step t608 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule implies :premises (t607))
% 3.73/4.02  (step t609 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t608 a2))
% 3.73/4.02  (step t610 (cl (=> (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t611)
% 3.73/4.02  (assume t611.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t611.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.least_upper_bound tptp.a tptp.identity)) (:= Z (tptp.least_upper_bound tptp.a tptp.identity))))
% 3.73/4.02  (step t611.t2 (cl (not (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule or :premises (t611.t1))
% 3.73/4.02  (step t611.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t611.t2 t611.a0))
% 3.73/4.02  (step t611 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule subproof :discharge (t611.a0))
% 3.73/4.02  (step t612 (cl (=> (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t610 t611))
% 3.73/4.02  (step t613 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 3.73/4.02  (step t614 (cl (=> (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t612 t613))
% 3.73/4.02  (step t615 (cl (=> (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule contraction :premises (t614))
% 3.73/4.02  (step t616 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies :premises (t615))
% 3.73/4.02  (step t617 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t616 a2))
% 3.73/4.02  (step t618 (cl (=> (forall ((X $$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.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t619)
% 3.73/4.02  (assume t619.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t619.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.inverse tptp.a)) (:= Z (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.73/4.02  (step t619.t2 (cl (not (forall ((X $$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.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule or :premises (t619.t1))
% 3.73/4.02  (step t619.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t619.t2 t619.a0))
% 3.73/4.02  (step t619 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule subproof :discharge (t619.a0))
% 3.73/4.02  (step t620 (cl (=> (forall ((X $$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.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t618 t619))
% 3.73/4.02  (step t621 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t622 (cl (=> (forall ((X $$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.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule resolution :premises (t620 t621))
% 3.73/4.02  (step t623 (cl (=> (forall ((X $$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.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule contraction :premises (t622))
% 3.73/4.02  (step t624 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies :premises (t623))
% 3.73/4.02  (step t625 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t624 a2))
% 3.73/4.02  (step t626 (cl (=> (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t627)
% 3.73/4.02  (assume t627.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t627.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.least_upper_bound tptp.a tptp.identity)) (:= Z tptp.a)))
% 3.73/4.02  (step t627.t2 (cl (not (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule or :premises (t627.t1))
% 3.73/4.02  (step t627.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule resolution :premises (t627.t2 t627.a0))
% 3.73/4.02  (step t627 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule subproof :discharge (t627.a0))
% 3.73/4.02  (step t628 (cl (=> (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule resolution :premises (t626 t627))
% 3.73/4.02  (step t629 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t630 (cl (=> (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))))) :rule resolution :premises (t628 t629))
% 3.73/4.02  (step t631 (cl (=> (forall ((X $$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.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))))) :rule contraction :premises (t630))
% 3.73/4.02  (step t632 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule implies :premises (t631))
% 3.73/4.02  (step t633 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) tptp.a) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule resolution :premises (t632 a2))
% 3.73/4.02  (step t634 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t635)
% 3.73/4.02  (assume t635.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 3.73/4.02  (step t635.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.73/4.02  (step t635.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule or :premises (t635.t1))
% 3.73/4.02  (step t635.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t635.t2 t635.a0))
% 3.73/4.02  (step t635 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule subproof :discharge (t635.a0))
% 3.73/4.02  (step t636 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t634 t635))
% 3.73/4.02  (step t637 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t638 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t636 t637))
% 3.73/4.02  (step t639 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule contraction :premises (t638))
% 3.73/4.02  (step t640 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule implies :premises (t639))
% 3.73/4.02  (step t641 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply tptp.identity (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t640 t304))
% 3.73/4.02  (step t642 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t643)
% 3.73/4.02  (assume t643.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 3.73/4.02  (step t643.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a)))))
% 3.73/4.02  (step t643.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) :rule or :premises (t643.t1))
% 3.73/4.02  (step t643.t3 (cl (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t643.t2 t643.a0))
% 3.73/4.02  (step t643 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) :rule subproof :discharge (t643.a0))
% 3.73/4.02  (step t644 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t642 t643))
% 3.73/4.02  (step t645 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t646 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t644 t645))
% 3.73/4.02  (step t647 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t646))
% 3.73/4.02  (step t648 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) :rule implies :premises (t647))
% 3.73/4.02  (step t649 (cl (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.multiply tptp.identity (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t648 t304))
% 3.73/4.02  (step t650 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t651)
% 3.73/4.02  (assume t651.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 3.73/4.02  (step t651.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a)))
% 3.73/4.02  (step t651.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule or :premises (t651.t1))
% 3.73/4.02  (step t651.t3 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t651.t2 t651.a0))
% 3.73/4.02  (step t651 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule subproof :discharge (t651.a0))
% 3.73/4.02  (step t652 (cl (=> (forall ((X $$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 (t650 t651))
% 3.73/4.02  (step t653 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t654 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t652 t653))
% 3.73/4.02  (step t655 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule contraction :premises (t654))
% 3.73/4.02  (step t656 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule implies :premises (t655))
% 3.73/4.02  (step t657 (cl (not (= (forall ((X $$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 $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule equiv_pos2)
% 3.73/4.02  (anchor :step t658 :args ((X $$unsorted) (:= X X)))
% 3.73/4.02  (step t658.t1 (cl (= X X)) :rule refl)
% 3.73/4.02  (step t658.t2 (cl (= (= (tptp.inverse (tptp.inverse X)) X) (= X (tptp.inverse (tptp.inverse X))))) :rule all_simplify)
% 3.73/4.02  (step t658 (cl (= (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))) :rule bind)
% 3.73/4.02  (step t659 (cl (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule resolution :premises (t657 t658 a16))
% 3.73/4.02  (step t660 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t656 t659))
% 3.73/4.02  (step t661 (cl (=> (forall ((Y $$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.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t662)
% 3.73/4.02  (assume t662.a0 (forall ((Y $$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)))))
% 3.73/4.02  (step t662.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= Y (tptp.inverse tptp.a)) (:= Z (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (:= X (tptp.least_upper_bound tptp.a tptp.identity))))
% 3.73/4.02  (step t662.t2 (cl (not (forall ((Y $$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.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule or :premises (t662.t1))
% 3.73/4.02  (step t662.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t662.t2 t662.a0))
% 3.73/4.02  (step t662 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule subproof :discharge (t662.a0))
% 3.73/4.02  (step t663 (cl (=> (forall ((Y $$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.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t661 t662))
% 3.73/4.02  (step t664 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 3.73/4.02  (step t665 (cl (=> (forall ((Y $$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.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t663 t664))
% 3.73/4.02  (step t666 (cl (=> (forall ((Y $$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.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule contraction :premises (t665))
% 3.73/4.02  (step t667 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies :premises (t666))
% 3.73/4.02  (step t668 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t667 a14))
% 3.73/4.02  (step t669 (cl (=> (forall ((Y $$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.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t670)
% 3.73/4.02  (assume t670.a0 (forall ((Y $$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)))))
% 3.73/4.02  (step t670.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule forall_inst :args ((:= Y (tptp.inverse tptp.a)) (:= Z tptp.identity) (:= X tptp.a)))
% 3.73/4.02  (step t670.t2 (cl (not (forall ((Y $$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.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule or :premises (t670.t1))
% 3.73/4.02  (step t670.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t670.t2 t670.a0))
% 3.73/4.02  (step t670 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule subproof :discharge (t670.a0))
% 3.73/4.02  (step t671 (cl (=> (forall ((Y $$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.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t669 t670))
% 3.73/4.02  (step t672 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t673 (cl (=> (forall ((Y $$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.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t671 t672))
% 3.73/4.02  (step t674 (cl (=> (forall ((Y $$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.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a))))) :rule contraction :premises (t673))
% 3.73/4.02  (step t675 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule implies :premises (t674))
% 3.73/4.02  (step t676 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t675 a13))
% 3.73/4.02  (step t677 (cl (=> (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t678)
% 3.73/4.02  (assume t678.a0 (forall ((Y $$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)))))
% 3.73/4.02  (step t678.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (:= X tptp.identity)))
% 3.73/4.02  (step t678.t2 (cl (not (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule or :premises (t678.t1))
% 3.73/4.02  (step t678.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule resolution :premises (t678.t2 t678.a0))
% 3.73/4.02  (step t678 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule subproof :discharge (t678.a0))
% 3.73/4.02  (step t679 (cl (=> (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule resolution :premises (t677 t678))
% 3.73/4.02  (step t680 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))))) :rule implies_neg2)
% 3.73/4.02  (step t681 (cl (=> (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))))) :rule resolution :premises (t679 t680))
% 3.73/4.02  (step t682 (cl (=> (forall ((Y $$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.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity))))) :rule contraction :premises (t681))
% 3.73/4.02  (step t683 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule implies :premises (t682))
% 3.73/4.02  (step t684 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity) (tptp.least_upper_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)))) :rule resolution :premises (t683 a13))
% 3.73/4.02  (step t685 (cl (=> (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t686)
% 3.73/4.02  (assume t686.a0 (forall ((X $$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)))))
% 3.73/4.02  (step t686.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= Y (tptp.least_upper_bound tptp.a tptp.identity)) (:= Z tptp.a)))
% 3.73/4.02  (step t686.t2 (cl (not (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule or :premises (t686.t1))
% 3.73/4.02  (step t686.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t686.t2 t686.a0))
% 3.73/4.02  (step t686 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule subproof :discharge (t686.a0))
% 3.73/4.02  (step t687 (cl (=> (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t685 t686))
% 3.73/4.02  (step t688 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t689 (cl (=> (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t687 t688))
% 3.73/4.02  (step t690 (cl (=> (forall ((X $$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.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule contraction :premises (t689))
% 3.73/4.02  (step t691 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule implies :premises (t690))
% 3.73/4.02  (step t692 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t691 a12))
% 3.73/4.02  (step t693 (cl (=> (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t694)
% 3.73/4.02  (assume t694.a0 (forall ((X $$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)))))
% 3.73/4.02  (step t694.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (:= Z (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.73/4.02  (step t694.t2 (cl (not (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule or :premises (t694.t1))
% 3.73/4.02  (step t694.t3 (cl (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t694.t2 t694.a0))
% 3.73/4.02  (step t694 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule subproof :discharge (t694.a0))
% 3.73/4.02  (step t695 (cl (=> (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t693 t694))
% 3.73/4.02  (step t696 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t697 (cl (=> (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule resolution :premises (t695 t696))
% 3.73/4.02  (step t698 (cl (=> (forall ((X $$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.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))))) :rule contraction :premises (t697))
% 3.73/4.02  (step t699 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies :premises (t698))
% 3.73/4.02  (step t700 (cl (= (tptp.multiply tptp.a (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))) (tptp.greatest_lower_bound (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t699 a12))
% 3.73/4.02  (step t701 (cl (=> (forall ((X $$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.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t702)
% 3.73/4.02  (assume t702.a0 (forall ((X $$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)))))
% 3.73/4.02  (step t702.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.a) (:= Z tptp.identity)))
% 3.73/4.02  (step t702.t2 (cl (not (forall ((X $$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.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule or :premises (t702.t1))
% 3.73/4.02  (step t702.t3 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t702.t2 t702.a0))
% 3.73/4.02  (step t702 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule subproof :discharge (t702.a0))
% 3.73/4.02  (step t703 (cl (=> (forall ((X $$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.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t701 t702))
% 3.73/4.02  (step t704 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule implies_neg2)
% 3.73/4.02  (step t705 (cl (=> (forall ((X $$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.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t703 t704))
% 3.73/4.02  (step t706 (cl (=> (forall ((X $$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.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity))))) :rule contraction :premises (t705))
% 3.73/4.02  (step t707 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule implies :premises (t706))
% 3.73/4.02  (step t708 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t707 a11))
% 3.73/4.02  (step t709 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t710)
% 3.73/4.02  (assume t710.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 3.73/4.02  (step t710.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))
% 3.73/4.02  (step t710.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule or :premises (t710.t1))
% 3.73/4.02  (step t710.t3 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t710.t2 t710.a0))
% 3.73/4.02  (step t710 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule subproof :discharge (t710.a0))
% 3.73/4.02  (step t711 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t709 t710))
% 3.73/4.02  (step t712 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule implies_neg2)
% 3.73/4.02  (step t713 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule resolution :premises (t711 t712))
% 3.73/4.02  (step t714 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))))) :rule contraction :premises (t713))
% 3.73/4.02  (step t715 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies :premises (t714))
% 3.73/4.02  (step t716 (cl (not (= (forall ((X $$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 $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule equiv_pos2)
% 3.73/4.02  (anchor :step t717 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 3.73/4.02  (step t717.t1 (cl (= X X)) :rule refl)
% 3.73/4.02  (step t717.t2 (cl (= Y Y)) :rule refl)
% 3.73/4.02  (step t717.t3 (cl (= (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule all_simplify)
% 3.73/4.02  (step t717 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))) :rule bind)
% 3.73/4.02  (step t718 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule resolution :premises (t716 t717 a10))
% 3.73/4.02  (step t719 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t715 t718))
% 3.73/4.02  (step t720 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t721)
% 3.73/4.02  (assume t721.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 3.73/4.02  (step t721.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.least_upper_bound tptp.identity tptp.a))))
% 3.73/4.02  (step t721.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule or :premises (t721.t1))
% 3.73/4.02  (step t721.t3 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule resolution :premises (t721.t2 t721.a0))
% 3.73/4.02  (step t721 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule subproof :discharge (t721.a0))
% 3.73/4.02  (step t722 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule resolution :premises (t720 t721))
% 3.73/4.02  (step t723 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (not (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t724 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule resolution :premises (t722 t723))
% 3.73/4.02  (step t725 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))))) :rule contraction :premises (t724))
% 3.73/4.02  (step t726 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule implies :premises (t725))
% 3.73/4.02  (step t727 (cl (= tptp.identity (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule resolution :premises (t726 t339))
% 3.73/4.02  (step t728 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t729)
% 3.73/4.02  (assume t729.a0 (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))
% 3.73/4.02  (step t729.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 3.73/4.02  (step t729.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule or :premises (t729.t1))
% 3.73/4.02  (step t729.t3 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t729.t2 t729.a0))
% 3.73/4.02  (step t729 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule subproof :discharge (t729.a0))
% 3.73/4.02  (step t730 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t728 t729))
% 3.73/4.02  (step t731 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule implies_neg2)
% 3.73/4.02  (step t732 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t730 t731))
% 3.73/4.02  (step t733 (cl (=> (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule contraction :premises (t732))
% 3.73/4.02  (step t734 (cl (not (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule implies :premises (t733))
% 3.73/4.02  (step t735 (cl (not (= (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))) (not (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X))) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule equiv_pos2)
% 3.73/4.02  (anchor :step t736 :args ((X $$unsorted) (:= X X)))
% 3.73/4.02  (step t736.t1 (cl (= X X)) :rule refl)
% 3.73/4.02  (step t736.t2 (cl (= (= (tptp.greatest_lower_bound X X) X) (= X (tptp.greatest_lower_bound X X)))) :rule all_simplify)
% 3.73/4.02  (step t736 (cl (= (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)) (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X))))) :rule bind)
% 3.73/4.02  (step t737 (cl (forall ((X $$unsorted)) (= X (tptp.greatest_lower_bound X X)))) :rule resolution :premises (t735 t736 a8))
% 3.73/4.02  (step t738 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t734 t737))
% 3.73/4.02  (step t739 (cl (=> (forall ((X $$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))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t740)
% 3.73/4.02  (assume t740.a0 (forall ((X $$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))))
% 3.73/4.02  (step t740.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) (:= Z tptp.identity)))
% 3.73/4.02  (step t740.t2 (cl (not (forall ((X $$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)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule or :premises (t740.t1))
% 3.73/4.02  (step t740.t3 (cl (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule resolution :premises (t740.t2 t740.a0))
% 3.73/4.02  (step t740 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule subproof :discharge (t740.a0))
% 3.73/4.02  (step t741 (cl (=> (forall ((X $$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))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule resolution :premises (t739 t740))
% 3.73/4.02  (step t742 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)))) :rule implies_neg2)
% 3.73/4.02  (step t743 (cl (=> (forall ((X $$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))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)))) :rule resolution :premises (t741 t742))
% 3.73/4.02  (step t744 (cl (=> (forall ((X $$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))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity)))) :rule contraction :premises (t743))
% 3.73/4.02  (step t745 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule implies :premises (t744))
% 3.73/4.02  (step t746 (cl (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) tptp.identity)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))) tptp.identity))) :rule resolution :premises (t745 a6))
% 3.73/4.02  (step t747 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t748)
% 3.73/4.02  (assume t748.a0 (forall ((X $$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))))
% 3.73/4.02  (step t748.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (:= Y (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (:= Z (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))
% 3.73/4.02  (step t748.t2 (cl (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule or :premises (t748.t1))
% 3.73/4.02  (step t748.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t748.t2 t748.a0))
% 3.73/4.02  (step t748 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule subproof :discharge (t748.a0))
% 3.73/4.02  (step t749 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t747 t748))
% 3.73/4.02  (step t750 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t751 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule resolution :premises (t749 t750))
% 3.73/4.02  (step t752 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule contraction :premises (t751))
% 3.73/4.02  (step t753 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule implies :premises (t752))
% 3.73/4.02  (step t754 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t753 a5))
% 3.73/4.02  (step t755 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t756)
% 3.73/4.02  (assume t756.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 3.73/4.02  (step t756.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))))
% 3.73/4.02  (step t756.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule or :premises (t756.t1))
% 3.73/4.02  (step t756.t3 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule resolution :premises (t756.t2 t756.a0))
% 3.73/4.02  (step t756 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule subproof :discharge (t756.a0))
% 3.73/4.02  (step t757 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule resolution :premises (t755 t756))
% 3.73/4.02  (step t758 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (not (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)))) :rule implies_neg2)
% 3.73/4.02  (step t759 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)))) :rule resolution :premises (t757 t758))
% 3.73/4.02  (step t760 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity)))) :rule contraction :premises (t759))
% 3.73/4.02  (step t761 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule implies :premises (t760))
% 3.73/4.02  (step t762 (cl (= (tptp.least_upper_bound tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.identity))) :rule resolution :premises (t761 a4))
% 3.73/4.02  (step t763 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t764)
% 3.73/4.02  (assume t764.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 3.73/4.02  (step t764.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (:= Y (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))
% 3.73/4.02  (step t764.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t764.t1))
% 3.73/4.02  (step t764.t3 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t764.t2 t764.a0))
% 3.73/4.02  (step t764 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t764.a0))
% 3.73/4.02  (step t765 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t763 t764))
% 3.73/4.02  (step t766 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t767 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t765 t766))
% 3.73/4.02  (step t768 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t767))
% 3.73/4.02  (step t769 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t768))
% 3.73/4.02  (step t770 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t769 a3))
% 3.73/4.02  (step t771 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t772)
% 3.73/4.02  (assume t772.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t772.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.inverse tptp.a)) (:= Z (tptp.inverse (tptp.inverse tptp.a)))))
% 3.73/4.02  (step t772.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule or :premises (t772.t1))
% 3.73/4.02  (step t772.t3 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t772.t2 t772.a0))
% 3.73/4.02  (step t772 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule subproof :discharge (t772.a0))
% 3.73/4.02  (step t773 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t771 t772))
% 3.73/4.02  (step t774 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule implies_neg2)
% 3.73/4.02  (step t775 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule resolution :premises (t773 t774))
% 3.73/4.02  (step t776 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))))) :rule contraction :premises (t775))
% 3.73/4.02  (step t777 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies :premises (t776))
% 3.73/4.02  (step t778 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply tptp.a (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t777 a2))
% 3.73/4.02  (step t779 (cl (=> (forall ((X $$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.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t780)
% 3.73/4.02  (assume t780.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t780.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.inverse (tptp.inverse tptp.a))) (:= Z (tptp.inverse tptp.a))))
% 3.73/4.02  (step t780.t2 (cl (not (forall ((X $$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.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule or :premises (t780.t1))
% 3.73/4.02  (step t780.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t780.t2 t780.a0))
% 3.73/4.02  (step t780 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule subproof :discharge (t780.a0))
% 3.73/4.02  (step t781 (cl (=> (forall ((X $$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.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t779 t780))
% 3.73/4.02  (step t782 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t783 (cl (=> (forall ((X $$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.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule resolution :premises (t781 t782))
% 3.73/4.02  (step t784 (cl (=> (forall ((X $$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.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule contraction :premises (t783))
% 3.73/4.02  (step t785 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies :premises (t784))
% 3.73/4.02  (step t786 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t785 a2))
% 3.73/4.02  (step t787 (cl (=> (forall ((X $$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 $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t788)
% 3.73/4.02  (assume t788.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 3.73/4.02  (step t788.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 3.73/4.02  (step t788.t2 (cl (not (forall ((X $$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 (t788.t1))
% 3.73/4.02  (step t788.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t788.t2 t788.a0))
% 3.73/4.02  (step t788 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule subproof :discharge (t788.a0))
% 3.73/4.02  (step t789 (cl (=> (forall ((X $$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 (t787 t788))
% 3.73/4.02  (step t790 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t791 (cl (=> (forall ((X $$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 $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t789 t790))
% 3.73/4.02  (step t792 (cl (=> (forall ((X $$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 (t791))
% 3.73/4.02  (step t793 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule implies :premises (t792))
% 3.73/4.02  (step t794 (cl (not (= (forall ((X $$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 $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule equiv_pos2)
% 3.73/4.02  (anchor :step t795 :args ((X $$unsorted) (:= X X)))
% 3.73/4.02  (step t795.t1 (cl (= X X)) :rule refl)
% 3.73/4.02  (step t795.t2 (cl (= (= (tptp.multiply (tptp.inverse X) X) tptp.identity) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule all_simplify)
% 3.73/4.02  (step t795 (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)
% 3.73/4.02  (step t796 (cl (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule resolution :premises (t794 t795 a1))
% 3.73/4.02  (step t797 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t793 t796))
% 3.73/4.02  (step t798 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t799)
% 3.73/4.02  (assume t799.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 3.73/4.02  (step t799.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 3.73/4.02  (step t799.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule or :premises (t799.t1))
% 3.73/4.02  (step t799.t3 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t799.t2 t799.a0))
% 3.73/4.02  (step t799 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule subproof :discharge (t799.a0))
% 3.73/4.02  (step t800 (cl (=> (forall ((X $$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 (t798 t799))
% 3.73/4.02  (step t801 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t802 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t800 t801))
% 3.73/4.02  (step t803 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule contraction :premises (t802))
% 3.73/4.02  (step t804 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule implies :premises (t803))
% 3.73/4.02  (step t805 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t804 t304))
% 3.73/4.02  (step t806 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t807)
% 3.73/4.02  (assume t807.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 3.73/4.02  (step t807.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.a)))
% 3.73/4.02  (step t807.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule or :premises (t807.t1))
% 3.73/4.02  (step t807.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t807.t2 t807.a0))
% 3.73/4.02  (step t807 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule subproof :discharge (t807.a0))
% 3.73/4.02  (step t808 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t806 t807))
% 3.73/4.02  (step t809 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t810 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t808 t809))
% 3.73/4.02  (step t811 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t810))
% 3.73/4.02  (step t812 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule implies :premises (t811))
% 3.73/4.02  (step t813 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t812 a17))
% 3.73/4.02  (step t814 (cl (=> (forall ((Y $$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.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t815)
% 3.73/4.02  (assume t815.a0 (forall ((Y $$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)))))
% 3.73/4.02  (step t815.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule forall_inst :args ((:= Y (tptp.inverse tptp.a)) (:= Z (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= X tptp.a)))
% 3.73/4.02  (step t815.t2 (cl (not (forall ((Y $$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.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule or :premises (t815.t1))
% 3.73/4.02  (step t815.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t815.t2 t815.a0))
% 3.73/4.02  (step t815 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule subproof :discharge (t815.a0))
% 3.73/4.02  (step t816 (cl (=> (forall ((Y $$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.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t814 t815))
% 3.73/4.02  (step t817 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t818 (cl (=> (forall ((Y $$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.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule resolution :premises (t816 t817))
% 3.73/4.02  (step t819 (cl (=> (forall ((Y $$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.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a))))) :rule contraction :premises (t818))
% 3.73/4.02  (step t820 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule implies :premises (t819))
% 3.73/4.02  (step t821 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.a) tptp.a) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) tptp.a)))) :rule resolution :premises (t820 a14))
% 3.73/4.02  (step t822 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t823)
% 3.73/4.02  (assume t823.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 3.73/4.02  (step t823.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.inverse tptp.a))))
% 3.73/4.02  (step t823.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule or :premises (t823.t1))
% 3.73/4.02  (step t823.t3 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t823.t2 t823.a0))
% 3.73/4.02  (step t823 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule subproof :discharge (t823.a0))
% 3.73/4.02  (step t824 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t822 t823))
% 3.73/4.02  (step t825 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 3.73/4.02  (step t826 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule resolution :premises (t824 t825))
% 3.73/4.02  (step t827 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))))) :rule contraction :premises (t826))
% 3.73/4.02  (step t828 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule implies :premises (t827))
% 3.73/4.02  (step t829 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t828 t718))
% 3.73/4.02  (step t830 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t831)
% 3.73/4.02  (assume t831.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 3.73/4.02  (step t831.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 3.73/4.02  (step t831.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) :rule or :premises (t831.t1))
% 3.73/4.02  (step t831.t3 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) :rule resolution :premises (t831.t2 t831.a0))
% 3.73/4.02  (step t831 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) :rule subproof :discharge (t831.a0))
% 3.73/4.02  (step t832 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) :rule resolution :premises (t830 t831))
% 3.73/4.02  (step t833 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (not (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule implies_neg2)
% 3.73/4.02  (step t834 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule resolution :premises (t832 t833))
% 3.73/4.02  (step t835 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a))))) :rule contraction :premises (t834))
% 3.73/4.02  (step t836 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) :rule implies :premises (t835))
% 3.73/4.02  (step t837 (cl (= tptp.identity (tptp.greatest_lower_bound tptp.identity (tptp.least_upper_bound tptp.identity tptp.a)))) :rule resolution :premises (t836 t718))
% 3.73/4.02  (step t838 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t839)
% 3.73/4.02  (assume t839.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 3.73/4.02  (step t839.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.least_upper_bound tptp.a tptp.identity))))
% 3.73/4.02  (step t839.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule or :premises (t839.t1))
% 3.73/4.02  (step t839.t3 (cl (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t839.t2 t839.a0))
% 3.73/4.02  (step t839 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule subproof :discharge (t839.a0))
% 3.73/4.02  (step t840 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t838 t839))
% 3.73/4.02  (step t841 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (not (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule implies_neg2)
% 3.73/4.02  (step t842 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule resolution :premises (t840 t841))
% 3.73/4.02  (step t843 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))))) :rule contraction :premises (t842))
% 3.73/4.02  (step t844 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies :premises (t843))
% 3.73/4.02  (step t845 (cl (= tptp.a (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t844 t339))
% 3.73/4.02  (step t846 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t847)
% 3.73/4.02  (assume t847.a0 (forall ((X $$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))))
% 3.73/4.02  (step t847.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (:= Z (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 3.73/4.02  (step t847.t2 (cl (not (forall ((X $$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)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule or :premises (t847.t1))
% 3.73/4.02  (step t847.t3 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t847.t2 t847.a0))
% 3.73/4.02  (step t847 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule subproof :discharge (t847.a0))
% 3.73/4.02  (step t848 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t846 t847))
% 3.73/4.02  (step t849 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule implies_neg2)
% 3.73/4.02  (step t850 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t848 t849))
% 3.73/4.02  (step t851 (cl (=> (forall ((X $$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))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule contraction :premises (t850))
% 3.73/4.02  (step t852 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule implies :premises (t851))
% 3.73/4.02  (step t853 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))) (tptp.greatest_lower_bound (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t852 a5))
% 3.73/4.02  (step t854 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t855)
% 3.73/4.02  (assume t855.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 3.73/4.02  (step t855.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.least_upper_bound tptp.a tptp.identity))))
% 3.73/4.02  (step t855.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule or :premises (t855.t1))
% 3.73/4.02  (step t855.t3 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule resolution :premises (t855.t2 t855.a0))
% 3.73/4.02  (step t855 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule subproof :discharge (t855.a0))
% 3.73/4.02  (step t856 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule resolution :premises (t854 t855))
% 3.73/4.02  (step t857 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule implies_neg2)
% 3.73/4.02  (step t858 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule resolution :premises (t856 t857))
% 3.73/4.02  (step t859 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a)))) :rule contraction :premises (t858))
% 3.73/4.02  (step t860 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule implies :premises (t859))
% 3.73/4.02  (step t861 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) tptp.a))) :rule resolution :premises (t860 a3))
% 3.73/4.02  (step t862 (cl (=> (forall ((X $$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.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t863)
% 3.73/4.02  (assume t863.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 3.73/4.02  (step t863.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.a) (:= Z tptp.identity)))
% 3.73/4.02  (step t863.t2 (cl (not (forall ((X $$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.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule or :premises (t863.t1))
% 3.73/4.02  (step t863.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t863.t2 t863.a0))
% 3.73/4.02  (step t863 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule subproof :discharge (t863.a0))
% 3.73/4.02  (step t864 (cl (=> (forall ((X $$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.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t862 t863))
% 3.73/4.02  (step t865 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule implies_neg2)
% 3.73/4.02  (step t866 (cl (=> (forall ((X $$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.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule resolution :premises (t864 t865))
% 3.73/4.02  (step t867 (cl (=> (forall ((X $$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.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity))))) :rule contraction :premises (t866))
% 3.73/4.02  (step t868 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule implies :premises (t867))
% 3.73/4.02  (step t869 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply tptp.a tptp.identity)))) :rule resolution :premises (t868 a2))
% 3.73/4.02  (step t870 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t871)
% 3.73/4.02  (assume t871.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 3.73/4.02  (step t871.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.identity)))
% 3.73/4.02  (step t871.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule or :premises (t871.t1))
% 3.73/4.02  (step t871.t3 (cl (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t871.t2 t871.a0))
% 3.73/4.02  (step t871 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule subproof :discharge (t871.a0))
% 3.73/4.02  (step t872 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t870 t871))
% 3.73/4.02  (step t873 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (not (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule implies_neg2)
% 3.73/4.02  (step t874 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule resolution :premises (t872 t873))
% 3.73/4.02  (step t875 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule contraction :premises (t874))
% 3.73/4.02  (step t876 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule implies :premises (t875))
% 3.73/4.02  (step t877 (cl (= (tptp.inverse tptp.a) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)))) :rule resolution :premises (t876 t718))
% 3.73/4.02  (step t878 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t879)
% 3.73/4.02  (assume t879.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 3.73/4.02  (step t879.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.identity)))
% 3.73/4.02  (step t879.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule or :premises (t879.t1))
% 3.73/4.02  (step t879.t3 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t879.t2 t879.a0))
% 3.73/4.02  (step t879 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule subproof :discharge (t879.a0))
% 3.73/4.02  (step t880 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t878 t879))
% 3.73/4.02  (step t881 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 3.73/4.02  (step t882 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t880 t881))
% 3.73/4.02  (step t883 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity))))) :rule contraction :premises (t882))
% 3.73/4.02  (step t884 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule implies :premises (t883))
% 3.73/4.02  (step t885 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t884 t718))
% 3.73/4.02  (step t886 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 3.73/4.02  (anchor :step t887)
% 3.73/4.02  (assume t887.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 3.73/4.02  (step t887.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y tptp.identity)))
% 3.73/4.02  (step t887.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule or :premises (t887.t1))
% 3.73/4.02  (step t887.t3 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t887.t2 t887.a0))
% 3.73/4.02  (step t887 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule subproof :discharge (t887.a0))
% 3.73/4.02  (step t888 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t886 t887))
% 3.73/4.03  (step t889 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule implies_neg2)
% 3.73/4.03  (step t890 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t888 t889))
% 3.73/4.03  (step t891 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a))))) :rule contraction :premises (t890))
% 3.73/4.03  (step t892 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule implies :premises (t891))
% 3.73/4.03  (step t893 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t892 a4))
% 3.73/4.03  (step t894 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 3.73/4.03  (anchor :step t895)
% 3.73/4.03  (assume t895.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 3.73/4.03  (step t895.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.identity)))
% 3.73/4.03  (step t895.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) :rule or :premises (t895.t1))
% 3.73/4.03  (step t895.t3 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) :rule resolution :premises (t895.t2 t895.a0))
% 3.73/4.03  (step t895 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) :rule subproof :discharge (t895.a0))
% 3.73/4.03  (step t896 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) :rule resolution :premises (t894 t895))
% 3.73/4.03  (step t897 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)))) :rule implies_neg2)
% 3.73/4.03  (step t898 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)))) :rule resolution :premises (t896 t897))
% 3.73/4.03  (step t899 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a)))) :rule contraction :premises (t898))
% 3.73/4.03  (step t900 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) :rule implies :premises (t899))
% 3.73/4.03  (step t901 (cl (= (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound tptp.identity tptp.a))) :rule resolution :premises (t900 a4))
% 3.73/4.03  (step t902 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 3.73/4.03  (anchor :step t903)
% 3.73/4.03  (assume t903.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 3.73/4.03  (step t903.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.identity)) (:= Y (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))
% 3.73/4.03  (step t903.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule or :premises (t903.t1))
% 3.73/4.03  (step t903.t3 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t903.t2 t903.a0))
% 3.73/4.03  (step t903 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule subproof :discharge (t903.a0))
% 3.73/4.03  (step t904 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t902 t903))
% 3.73/4.03  (step t905 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule implies_neg2)
% 3.73/4.03  (step t906 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule resolution :premises (t904 t905))
% 3.73/4.03  (step t907 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity))))) :rule contraction :premises (t906))
% 3.73/4.03  (step t908 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule implies :premises (t907))
% 3.73/4.03  (step t909 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity) (tptp.least_upper_bound tptp.a tptp.identity)))) :rule resolution :premises (t908 a3))
% 3.73/4.03  (step t910 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 3.73/4.03  (anchor :step t911)
% 3.73/4.03  (assume t911.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 3.73/4.03  (step t911.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 3.73/4.03  (step t911.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule or :premises (t911.t1))
% 3.73/4.03  (step t911.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t911.t2 t911.a0))
% 3.73/4.03  (step t911 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule subproof :discharge (t911.a0))
% 3.73/4.03  (step t912 (cl (=> (forall ((X $$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 (t910 t911))
% 3.73/4.03  (step t913 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies_neg2)
% 3.73/4.03  (step t914 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t912 t913))
% 3.73/4.03  (step t915 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule contraction :premises (t914))
% 3.73/4.03  (step t916 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule implies :premises (t915))
% 3.73/4.03  (step t917 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t916 t796))
% 3.73/4.03  (step t918 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 3.73/4.03  (anchor :step t919)
% 3.73/4.03  (assume t919.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 3.73/4.03  (step t919.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity)))
% 3.73/4.03  (step t919.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule or :premises (t919.t1))
% 3.73/4.03  (step t919.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule resolution :premises (t919.t2 t919.a0))
% 3.73/4.03  (step t919 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule subproof :discharge (t919.a0))
% 3.73/4.03  (step t920 (cl (=> (forall ((X $$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 (t918 t919))
% 3.73/4.03  (step t921 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))) :rule implies_neg2)
% 3.73/4.03  (step t922 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))) :rule resolution :premises (t920 t921))
% 3.73/4.03  (step t923 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))) :rule contraction :premises (t922))
% 3.73/4.03  (step t924 (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 (t923))
% 3.73/4.03  (step t925 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule resolution :premises (t924 t796))
% 3.73/4.03  (step t926 (cl (not (= tptp.identity (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.identity) (tptp.least_upper_bound (tptp.inverse tptp.a) tptp.identity))))) :rule not_symm :premises (a18))
% 3.73/4.03  (step t927 (cl (= tptp.identity (tptp.inverse tptp.identity))) :rule symm :premises (a15))
% 3.73/4.03  (step t928 (cl) :rule resolution :premises (t270 t278 t286 t294 t305 t313 t321 t329 t340 t348 t356 t364 t372 t380 t388 t396 t404 t412 t420 t428 t436 t444 t452 t460 t468 t476 t484 t492 t500 t508 t516 t524 t532 t540 t548 t556 t564 t572 t585 t593 t601 t609 t617 t625 t633 t641 t649 t660 t668 t676 t684 t692 t700 t708 t719 t727 t738 t746 t754 t762 t770 t778 t786 t797 t805 t813 t821 t829 t837 t845 t853 t861 t869 t877 t885 t893 t901 t909 t917 t925 t926 t927))
% 3.73/4.03  
% 3.73/4.03  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.eo9kAMovwd/cvc5---1.0.5_9508.smt2
% 3.73/4.04  % cvc5---1.0.5 exiting
% 3.73/4.04  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------